{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "<img src=\"../../../img/ods_stickers.jpg\">\n",
    "## Открытый курс по машинному обучению\n",
    "<center>Автор материала: Алексей Григорьев (@ololo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.stats import beta\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "from IPython import display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi-Armed Bandit\n",
    "\n",
    "\n",
    "В этом туториале мы узнаем:\n",
    "\n",
    "- Что такое многорукий бандит\n",
    "- Как использовать теорему Байеса и Бета-распределение для решения этой задачи\n",
    "- Как работает RTB реклама\n",
    "- Что такое иерархические байесовы модели и как они используются для оптимизации рекламных показов\n",
    "- Как сложить иерархическую модель с бандитом и получить иерархию бандитов\n",
    "\n",
    "\n",
    "Начнем с небольшой теории.\n",
    "\n",
    "**Многорукий бандит** (или \"Multi-Armed Bandit\", если по-английски) - это игровой автомат, у которого имеется несколько \"рук\". Мы за руку дергаем и выигрываем с какой-то вероятностью, например, $\\theta_i$. Проблема в том, что вероятности нам не известны, поэтому мы хотим их выучить, взаимодействуя с бандитом, и при этом мы хотим свести количество проигрышей к минимуму.\n",
    "\n",
    "Допустим, у нас 1000 попыток и 5 рук. Что можно сделать? Дернуть каждую руку по 10 раз, записать количество успешных исходов для каждой руки (т.н. \"win rate\"), а потом все оставшиеся 950 раз дергать за руку с наилучшими показателями.\n",
    "\n",
    "Но вполне возможно, что нам просто повезло с какой-то рукой, и она просто по счастливой случайности выдала 10 выигрышей подряд. Такое ведь бывает, можно и монетку 10 раз подряд подбросить орлом верх.\n",
    "\n",
    "Тогда поступим следующим образом: отведём специальный бюджет для исследования среды: допустим, на каждые 10 попыток, 9 будем дергать за самую везучую руку (по-английски говорят \"exploit\"), а еще раз дёрнем случайно одну из 4-х других рук (а это называется \"explore\"). Если в какой-то момент мы заметили, что какая-то другая рука более везучая - переключаемся на неё, и начинаем именно её дергать (то есть эксплуатировать) 9 из 10 раз.\n",
    "\n",
    "Такой подход называется жадным подходом, или даже \"$\\varepsilon$-Greedy Bandit\", где $\\varepsilon$ - это параметр, бюджет, который мы отводим на исследование среды, в примере выше он равен 1/10 = 0.1, а все остальное время мы жадно дёргаем самую везучую руку.\n",
    "\n",
    "Так вот, говорят, такой подход неоптимальный и ведет к печали (или \"regret\", если по-английски). Причина в том, что когда нам даётся возможность поэкспериментировать, мы случайно выбираем руку, совсем не руководствуясь тем, как она себя вела в прошлом. Может, это очень плохая рука, и мы зря на неё тратим бюджет, и лучше дёрнуть какую-нибудь другую руку. Нам хотелось бы печаль свести к минимуму, а радость - к максимуму. Естественно, в этом нам поможет Байес (и его последователь Томпсон).\n",
    "\n",
    "**Байесовский Бандит** (или \"Bayesian Bernoulli Bandit\") использует теорему Байеса, поэтому давайте сначала её вспомним:\n",
    "\n",
    "$$P(\\theta \\mid x) = \\cfrac{P(x \\mid \\theta) \\ P(\\theta)}{P(x)}$$\n",
    "\n",
    "Тут у нас есть несколько частей:\n",
    "\n",
    "- $\\theta$ - это вероятность успешного исхода, то есть вероятность выиграть, нам неизвестна.\n",
    "- $x$ - исход взаимодействия с рукой бандита, успех или неудача (1 или 0), то, что мы можем увидеть. Именно это мы и используем, чтобы оценить $\\theta$.\n",
    "- $P(\\theta)$ - априорная вероятность, или \"prior\" - наше предположение о том, как $\\theta$ может быть распределена, это наши знания до того, как мы дернем руку\n",
    "- $P(x \\mid \\theta)$ - вероятность исхода $x$, принимая во внимание всё то, что мы знали о $\\theta$ на текущий момент, или \"likelihood\".\n",
    "- $P(\\theta \\mid x)$ - апостериорная вероятность, \"posterior\" - то, как изменится наше представление о руке, после того как мы увидели реализацию $x$.\n",
    "- $P(x)$ - полная вероятность наступления события $x$, не знаю, как по-английски, да и не важно это. Поэтому формулу чаще записывают таким образом:\n",
    "\n",
    "$$P(\\theta \\mid x) \\propto P(x \\mid \\theta) \\ P(\\theta)$$\n",
    "\n",
    "То есть для нас важны prior и likelihood, а $P(x)$ - это просто нормализующий фактор, чтобы posterior был функцией плотности вероятности (то есть интеграл этой функции должен быть равен 1).\n",
    "\n",
    "Так как исход у нас бинарный (удача/неудача), то моделировать исход $x$ будем с помощью функции Бернулли. Это наш likelihood:\n",
    "\n",
    "$$P(x \\mid \\theta) = \\theta^x \\ (1 - \\theta)^{1 - x}$$\n",
    "\n",
    "В качестве приора обычно выбирают Бета-распределение (оно же Beta distribution), которое определяется двумя параметрами $\\alpha$ и $\\beta$:\n",
    "\n",
    "$$P(\\theta) = \\cfrac{1}{B(\\alpha, \\beta)} \\theta^{\\alpha - 1} \\ (1 - \\theta)^{\\beta - 1}$$\n",
    "\n",
    "Почему именно Бета? Потому что Бета - сопряженное (conjugate) распределение с распределением Бернулли. То есть, если приор - Бета, а likelihood - Бернулли, то в результате у нас опять получится Бета. Это легко можно увидеть:\n",
    "\n",
    "$$P(x \\mid \\theta) \\times P(\\theta) \\propto \\Big( \\theta^x \\ (1 - \\theta)^{1 - x}\\Big)  \\times \\Big(\\theta^{\\alpha - 1} \\ (1 - \\theta)^{\\beta - 1}\\Big) = \\theta^{\\alpha - 1 + x} \\ (1 - \\theta)^{\\beta - 1 + (1 - x)}$$\n",
    "\n",
    "(Мы тут опустили некоторые детали - их можно посмотреть в любом учебнике по терверу.)\n",
    "\n",
    "То есть использование Беты позволяет нам очень легко обновлять апостериорное распределение:\n",
    "\n",
    "- если у нас успех, $x = 1$, то $\\alpha_\\text{post} = \\alpha + 1, \\beta_\\text{post} = \\beta$,\n",
    "- если у нас неудача, $x = 0$, то $\\alpha_\\text{post} = \\alpha, \\beta_\\text{post} = \\beta + 1$,\n",
    "- $\\alpha_\\text{post}$ и $\\beta_\\text{post}$ тут - параметры апостериорного распределение.\n",
    "\n",
    "После того, как мы дернули за руку и обновили параметры, апостериорное распределение становится априорным, и так после каждого эксперимента.\n",
    "\n",
    "Теперь перейдем к самому бандиту. Итак, каждая рука у нас - это $\\theta_i$, с приором $\\text{beta}(\\alpha_i, \\beta_i)$, где\n",
    "\n",
    "- $\\alpha_i$ - это количество успешных исходов на текущий момент (+1),\n",
    "- $\\beta_i$ - количество неуспешных (тоже +1).\n",
    "\n",
    "Перед тем, как мы дернули руку в самый первый раз, все $\\alpha_i = \\beta_i = 1$, что соответствует равномерному распределению от нуля до единицы - то есть мы совсем ничего о руках еще не знаем.\n",
    "\n",
    "Теперь алгоритм такой:\n",
    "\n",
    "- для каждой руки делаем выборку из $\\theta_i \\sim \\text{beta}(\\alpha_i, \\beta_i)$\n",
    "- выбираем руку, для которой значение семпла наибольшее, дёргаем именно за эту руку \n",
    "- наблюдаем результат, обновляем параметры для выбранной руки в зависимости от исхода\n",
    "- повторяем пока не надоест\n",
    "\n",
    "Этот алгоритм называется **Thompson Sampling** - именно такой способ обеспечивает оптимальное соотношение между expoitation и exploration, ведь в любой момент времени каждая рука может быть выбрана с ненулевой вероятностью, но не очень интересные руки будут выбраны реже. Мы увидем это ниже, когда реализуем бандита и посмотрим, как априорная вероятность меняется с течением времени. \n",
    "\n",
    "Если интересно как именно этот алгоритм минимизирует regret, то можно почитать \"A Tutorial on Thompson Sampling\" из списка источников. Или любую другую статью про бандитов, там тоже про это есть. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Реализация бандита\n",
    "\n",
    "Давайте теперь реализуем это на питоне. Создадим класс `Arm` - это будет рука бандита, внутри которой мы будем считать, сколько у нас было успешных попыток, и сколько было попыток всего. В любой момент времени мы можем попросить руку посчитать вероятность успеха, а так же обновить параметры."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Arm():\n",
    "    def __init__(self):\n",
    "        self.wins = 0\n",
    "        self.trials = 0\n",
    "\n",
    "    def sample(self):\n",
    "        a = 1 + self.wins\n",
    "        b = 1 + self.trials - self.wins\n",
    "        return beta.rvs(a=a, b=b)\n",
    "\n",
    "    def update(self, win):\n",
    "        self.trials = self.trials + 1\n",
    "        if win:\n",
    "            self.wins = self.wins + 1\n",
    "\n",
    "    def __repr__(self):\n",
    "        return 'arm (%d/%d)' % (self.wins, self.trials)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Почему вместо `alpha` и `beta` мы храним в классе `wins` и `trials`? Так удобнее обычно, именно поэтому.\n",
    "\n",
    "Бандит - это несколько рук, каждую из которых можно дёрнуть, поэтому давайте их сложим в список, это и будет наш бандит:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[arm (0/0), arm (0/0), arm (0/0)]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 3\n",
    "bandit = [Arm() for i in range(k)]\n",
    "bandit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Допустим, вероятность успеха рук задаётся следующим распределением:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "probs =  [0.65, 0.5, 0.4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь реализуем Thompson Sampling: на каждом шагу мы семплим все руки и дергаем ту, вероятность которой наибольшая - согласно семплу. И обновляем статистику после каждого шага."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[arm (30/44), arm (17/33), arm (10/23)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(4)\n",
    "random.seed(4)\n",
    "\n",
    "for i in range(100):\n",
    "    sample = [a.sample() for a in bandit]\n",
    "    best = np.argmax(sample)\n",
    "    win = random.random() <= probs[best]\n",
    "    bandit[best].update(win)\n",
    "\n",
    "bandit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Во время работы мы попробовали дернуть вторую и третью ручки, но чаще всего эксплуатировали самую первую руку - 44 раз.\n",
    "\n",
    "Давайте посмотрим, что происходит с распределениями. Для этого обнулим всю прошлую историю, и проследим, как априорное распределение каждой руки меняется с течением времени:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[arm (0/0), arm (0/0), arm (0/0)]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 3\n",
    "bandit = [Arm() for i in range(k)]\n",
    "bandit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "!rm animation/*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SxG95A2KUxC9cnyR+IYTzMThJnX6L2zfqEcLFSeK3o5s3b/Laa6/Rp08fgoOD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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efa9d9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(4)\n",
    "random.seed(4)\n",
    "\n",
    "colors = ['orange', 'blue', 'green']\n",
    "x = np.linspace(0, 1, 201)\n",
    "\n",
    "for i in range(200):\n",
    "    sample = [a.sample() for a in bandit]\n",
    "    best = np.argmax(sample)\n",
    "    win = random.random() <= probs[best]\n",
    "    bandit[best].update(win)\n",
    "\n",
    "    for p, arm, c in zip(probs, bandit, colors):\n",
    "        a = 1 + arm.wins\n",
    "        b = 1 + arm.trials - arm.wins\n",
    "\n",
    "        pdf = beta.pdf(x, a=a, b=b)\n",
    "\n",
    "        plt.plot(x, pdf, color=c, label='%d/%d, %0.2f' % (arm.wins, arm.trials, p))\n",
    "        plt.fill_between(x, pdf, color=c, alpha=0.1)\n",
    "        plt.vlines(p, 0, beta.pdf(p, a=a, b=b))\n",
    "\n",
    "\n",
    "    plt.legend(loc='upper left')\n",
    "    plt.ylim(0, 8)\n",
    "    plt.savefig('animation/iteration_%03d.png' % i)\n",
    "    plt.show()\n",
    "    display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "!/usr/bin/convert -loop 0 -delay 10 animation/* out.gif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"out.gif?01\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сначала мы дёргали вторую руку чаще других, потому что думали, что она самая успешная, но со временем выяснили, что третья рука вообще-то лучше, поэтому потом переключились на неё. Если присмотреться, то видно, что пересечение между распределенями ненулевое. Это означает, что в любой момент времени любая другая рука имеет ненулевую вероятность быть выбранной."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Реклама в RTB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "С простым бандитом разобрались. Теперь давайте немного отвлечёмся от бандита и поговорим о рекламе - ведь именно там бандиты часто используются.\n",
    "\n",
    "RTB, расшифровывается как Real Time Bidding, это режим аукционов в реальном времени. Каждый раз, когда пользователь открывает сайт с рекламой или приложение на телефоне, за кулисами за доли секунды разыгрывается небольшой аукцион, на котором рекламодатели соревнуются за возможность показать рекламу. \n",
    "\n",
    "Как это работает? Для примера рассмотрим рынок мобильной рекламы, но для веба и других рынков ситуация примерно такая же. \n",
    "\n",
    "Допустим, есть рекламодатель, который хочет порекламировать своё приложение, например, [Fidget Spinner](https://play.google.com/store/apps/details?id=com.ketchapp.fingerspinner) или какую-нибудь другую очень полезную программу для телефона. Рекламодатель обращается в DSP (Demand-Side Platform) - это компания, которая непосредсвенно участвует в аукционах, делает ставки и пытается продвинуть рекламируемое предложение. Это спрос на рекламу. Приложения, которые хотят у себя разместить рекламу, работают с SSP (Supply-Side Platform). SSP организуют аукционы, они создают предложение. SSP и DSP общаются друг с другом через RTB.\n",
    "\n",
    "Итак, SSP торгует рекламными местами в приложениях клиентов. Каждый раз, когда пользователь открывает какое-нибудь приложение, например, Angry Birds, ему показывается реклама. Чтобы решить, какую рекламу показать, Angry Birds отправляет запрос в SSP, где указывает \n",
    "\n",
    "- своё имя (то есть Angry Birds),\n",
    "- параметры рекламного места (баннер это или видео, размер баннера и т.п.),\n",
    "- какие-то сведения о пользователе (страна, информация о девайсе, и т.п.).\n",
    "\n",
    "SSP затем проводит аукцион (или не проводит, всякое бывает) - рассылает эту информацию нескольким DSP, каждый из которых назначает определённую цену за это рекламное место. Тот, кто больше всего заплатил, выигрывает возможность показать свою рекламу. После этого SSP отправляет эту рекламу обратно в приложение. В английской википедии (https://en.wikipedia.org/wiki/Online_advertising) про это достаточно подробно написано и красиво проиллюстрировано. \n",
    "\n",
    "Самое главное - всё это случается очень быстро, где-то в течение 100 мсек, поэтому если мы хотим использовать машин лернинг, наши модели должны уметь быстро регировать на запрос. То есть дип лернинг не получится использовать, но простые модели типа логистической регрессии - вполне. Про разные модели, которые используют в рекламе, можно почитать в книге \"Display Advertising with Real-Time Bidding (RTB) and Behavioural Targeting\". \n",
    "\n",
    "У логрега, однако, есть небольшой недостаток - он не очень хорошо умеет исследовать среду, exploration у него не очень, только exploitation есть. \n",
    "\n",
    "Попробую объяснить. Представим ситуацию - мы DSP и хотим участвовать в аукционе только тогда, когда вероятность клика высокая. Что мы делаем - тренируем модель, например, логрег, и говорим, что если модель предсказывает вероятность клика ниже какого-то порога (например, 0.02), то мы просто не участвуем в аукционе. \n",
    "\n",
    "Но 0.02 (2%) - это очень большое число для рекламы, большинство пользователей не кликает на рекламу вообще, поэтому \n",
    "таким образом мы отфильтруем большую часть входящего траффика. Вроде бы хорошо - мы тратим деньги только на потенциально полезных юзеров, которые нам принесут доход. \n",
    "\n",
    "Но есть одно \"но\" - когда мы захотим натренировать новую обновленную модель со свежими данными - модель увидит только часть данных! То есть мы откинем большую часть данных, и совсем не будем знать, что там происходит - вдруг часть этих юзеров изменят своё поведение? Мы об этом никогда не узнаем. Гугл про это даже статью написал, \"Machine Learning: The High Interest Credit Card of Technical Debt\", там они эту проблему называют \"Hidden Feedback Loops\".\n",
    "\n",
    "Можно попытаться решить проблему таким образом - если модель отдаёт предсказание выше порога, то мы ведем себя как обычно и участвуем в аукционе. Если ниже - то мы участвуем в аукционе с какой-нибудь вероятностью, например, 0.01. Таким образом мы только что изобрели аналог $\\varepsilon$-Greedy бандита, только для логрега. У которого такое же проблемы - вероятность среди плохих и более многообещающих пользователей одинаковая. \n",
    "\n",
    "Для бандитов эту проблему мы решили с помощью семплирования из Бета-распределения. Мы можем сделать то же самое! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hierarchical Models\n",
    "\n",
    "В ситуации с логрегом всё понятно - у нас есть какой-то набор признаков, типа страна, модель телефона, приложение, из которого приходит запрос, имя SSP, мы все это дело обрабатываем через One Hot Encoding, возможно взвешиваем признаки через TF-IDF или BM25, а потом запускаем `lr.fit(X, y)`. Всё, модель готова, можно интегрировать в прод. \n",
    "\n",
    "С Бетой немного сложнее. Представим, что у нас есть несколько наблюдений:\n",
    "\n",
    "- `[ru, iphone, angry_birds, 1]`\n",
    "- `[us, iphone, grindr, 0]`\n",
    "- `[ru, android, pornhub, 1]`\n",
    "\n",
    "Что можно сделать? Можно представить, что каждый набор признаков вида (страна, платформа, приложение) - это что-то типа \"руки\" бандита. То есть каждый такой набор помнит количество кликов и имеет своё распределение $\\text{beta}(\\alpha_i, \\beta_i)$.\n",
    "\n",
    "Приходит новый запрос, мы находим соотвествующую бету, берём из неё семпл, и говорим, что это и есть наш CTR. Если он больше порога, то мы участвуем в аукционе, меньше - не участвуем. Проблема логрега таким образом решается, потому что семпл может быть разным, и иногда он может оказаться выше порога. Логрег (по крайней мере обычный) так не умеет - он всегда предсказывает одну и ту же вероятность.\n",
    "\n",
    "Теперь представим, что появилось новое приложение, \"Beta Bandits\", и мы получили запрос вида `[ru, iphone, beta_bandits]`. Что делать? Информации про это приложение у нас нет, поэтому мы заводим новую бету с параметрами `(1, 1)` и начинаем собирать статистику по этому приложению. Но ведь у нас уже есть информация по пользователям из России с айфонами! Наверняка она была бы полезной, но с такой моделью мы никак эту информацию не можем использовать. А логрег бы смог.\n",
    "\n",
    "Для решения этой проблемы мы можем объединить признаки в иерархию. Например, так:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import graph_utils # файл graph_utils.py в этой же папке\n",
    "\n",
    "tree = {\n",
    "    'market': {\n",
    "        'ru': {\n",
    "            'iphone': ['angry_birds', 'beta_badits'],\n",
    "            'android': ['pornhub']\n",
    "        },\n",
    "        'us': {\n",
    "            'iphone': ['grindr'],\n",
    "        }, \n",
    "    }\n",
    "}\n",
    "\n",
    "g = graph_utils.tree_to_dot(tree)\n",
    "g.write_png('hierarchy.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"hierarchy.png?11\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Идея такая: более общие признаки находятся выше в иерархии, менее общие - ниже. Когда приходит запрос, мы спускаемся вниз по дереву, если каких-то признаков в пути нет, то мы добавляем нужные вершины. \n",
    "\n",
    "Каждая вершина этого графа хранит количество успехов и неудач, то есть $\\alpha_i$ и $\\beta_i$, которые мы используем для семлирования. Но перед тем, как сгенерировать предсказание, мы запрашиваем информацию у родительской вершины о её успехах и неудачах. Таким образом, если у нас появилась новая вершина, такая как \"beta_badits\", мы сможем воспользоваться накопленой статистикой из родительской вершины \"iphone\". Если вдруг появится какой-то пользователь с убунтуфоном, или, хуже того, с windows, мы добавим сразу две новые вершины в граф - \"windows\" и вершину с названием приложения. В этом случае мы воспользуемся статистикой, которую собрали в вершине \"ru\".\n",
    "\n",
    "Каким же образом вершины графа могут воспользоваться информацией из родителя? Конечно, с помощью приоров. \n",
    "\n",
    "В обычной ситуации, когда родителя нет, наша модель такая:\n",
    "\n",
    "- likelihood: $y \\mid \\theta \\sim \\text{bernoulli}(\\theta)$\n",
    "- prior: $\\theta \\sim \\text{beta}(\\alpha, \\beta)$\n",
    "\n",
    "А когда есть родитель $\\theta_p \\sim \\text{beta}(\\alpha_p, \\beta_p)$, то мы можем подключить параметры родителя следующим образом:\n",
    "\n",
    "- likelihood: $y \\mid \\theta \\sim \\text{bernoulli}(\\theta)$\n",
    "- prior: $\\theta \\mid \\alpha_p, \\beta_p \\sim \\text{beta}(\\alpha + \\alpha_p, \\beta + \\beta_p)$\n",
    "\n",
    "Однако когда в родителе накапливается достаточно большое количество статистики, значения родителя начинают \"перекрывать\" значения в ребёнке. \n",
    "\n",
    "Допустим, родитель хранит информацию о $N_p = \\alpha_p + \\beta_p$ испытаниях. Мы можем уменьшить влияние родителя, сделав семпл из испытаний родителя размера $n$, при этом $n$ должен быть небольшим числом. Таким образом, сначала, когда у ребёнка нет достаточной информации, мы пользуемся данными от родителя, но со временем он накопит достаточно данных, чтобы перекрыть приор родителя.\n",
    "\n",
    "Как сделать такой семпл? Например, так:\n",
    "\n",
    "- генерируем число $\\theta_p \\sim \\text{beta}(\\alpha_p, \\beta_p)$\n",
    "- принимаем его за среднее значение желаемого семла\n",
    "- тогда, $\\theta_p = \\alpha'_p\\, / \\, (\\alpha'_p + \\beta'_p)$, $n = \\alpha'_p + \\beta'_p$\n",
    "- из этого считаем $\\alpha'_p = \\theta_p \\, n$, $\\beta'_p = (1 - \\theta_p) \\, n$\n",
    "\n",
    "Теперь передаём именно эти значения $\\alpha'_p$ и $\\beta'_p$ ребёнку, поэтому приор у нас получается таким:\n",
    "\n",
    "- $\\theta \\mid \\alpha'_p, \\beta'_p \\sim \\text{beta}(\\alpha + \\alpha'_p, \\beta + \\beta'_p)$\n",
    "- $\\alpha'_p = \\theta_p \\, n$ и $\\beta'_p = (1 - \\theta_p) \\, n$\n",
    "- $\\theta_p \\sim \\text{beta}(\\alpha_p, \\beta_p)$\n",
    "\n",
    "В такой модели $n$ - это гиперпараметр, его обычно фиксируют. Он так же может быть случайной величиной, но тогда модель будет сложнее.\n",
    "\n",
    "Обновление в этой модели такое же, как у руки бандита: если пользователь в итоге кликнул, то мы увеличиваем параметр $\\alpha$, если нет - то $\\beta$. Отличие от рук состоит в том, что тут мы обновляем статистику у всех вершин, которые были на пути от корня дерева до листа. Если наши признаки были `[ru, iphone, angry_birds]`, то мы обновим счётчики для корня дерева, `ru`, `iphone` и `angry_birds`.\n",
    "\n",
    "И последнее, когда мы просим родителя дать нам информацию, нужно быть осторожным, чтобы случайно не посчитать одни и те же данные два раза. \n",
    "\n",
    "Представим, что в нашем графе только две вершины - родитель и ребёнок. Тогда ребёнку нет смысла просить родителя об информации, ведь у родителя нет ничего, о чём бы ребенок ещё не знал сам. \n",
    "\n",
    "А теперь представим другую ситуацию: у нас всего четыре вершины, родитель и три ребёнка. Тогда, когда первый ребёнок запрашивает информацию, то родитель должен использовать только данные, полученные от второго и третьего. Это делается очень легко: перед тем, как семплировать $\\theta_p$, мы для генерации используем $\\alpha = \\alpha_p - \\alpha_1$ и $\\beta = \\beta_p - \\beta_1$, где $p$ - это параметры родителя, а $1$ - первого ребёнка."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Реализация\n",
    "\n",
    "Давайте теперь реализуем это на питоне. Создадим класс `Node` со следующими параметрами:\n",
    "\n",
    "- `parent` - родительская вершина, у которой мы будем просить информацию, и\n",
    "- `downsample_size` - это $n$, про который мы писали выше.\n",
    "\n",
    "Как и в случае с бандитом, вместо `alpha` и `beta` мы храним `wins` и `trials`. \n",
    "\n",
    "Основные методы класса:\n",
    "\n",
    "- `sample_params_from_parent` - попросить родителя посчитать $\\alpha'_p$ и $\\beta'_p$\n",
    "- `sample` - вернуть семпл, почти как в бандите, но только ещё мы внутри вызываем `sample_params_from_parent`,\n",
    "- `update` - обновляет значения `wins` и `trials`.\n",
    "\n",
    "Так же у нас есть второстепенные методы:\n",
    "\n",
    "- `beta_params` - перевести `wins` и `trials` в $\\alpha$ и $\\beta$,\n",
    "- `no_data_in_parents` - проверить, есть ли у родителя какие-то данные, которых у нас ещё нет. Если есть, то можно просить параметры, а иначе смысла нет,\n",
    "- `total_trials` - посчитать общее количество попыток в модели.\n",
    "\n",
    "Так это выглядит в коде:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Node():\n",
    "    def __init__(self, name, parent=None, downsample_size=200):\n",
    "        \"\"\"\n",
    "        name: имя вершины\n",
    "        parent: родитель вершины, None если нет родителя\n",
    "        downsample_size: размер выборки при семплировании параметров из родителя,\n",
    "            по умолчанию наследуется от родительской вершины\n",
    "        \"\"\"\n",
    "        self.parent = parent\n",
    "\n",
    "        if parent is not None:\n",
    "            self.downsample_size = parent.downsample_size\n",
    "        else:\n",
    "            self.downsample_size = 200\n",
    "\n",
    "        self.name = name\n",
    "        self.wins = 0\n",
    "        self.trials = 0\n",
    "\n",
    "    def sample_params_from_parent(self, silent):\n",
    "        \"\"\"\n",
    "        делает выборку из родителя размером downsample_size и считает alpha и beta на основе этой выборки\n",
    "        если родителя нет, или у родителя нет данных, то возвращает alpha=0, beta=0\n",
    "\n",
    "        silent: вывод логов, False если нужны логи\n",
    "        \"\"\"\n",
    "        parent = self.parent\n",
    "        if parent is None:\n",
    "            return 0, 0\n",
    "\n",
    "        if self.no_data_in_parents():\n",
    "            return 0, 0\n",
    "\n",
    "        sample_size = min(self.downsample_size, self.total_trials())\n",
    "        parent_mean = parent.sample(w=self.wins, t=self.trials, silent=silent)\n",
    "\n",
    "        a_prior = parent_mean * sample_size\n",
    "        b_prior = sample_size - a_prior\n",
    "\n",
    "        if not silent:\n",
    "            print('prior %s->%s is %.3f: α=%.3f, β=%.3f' % (self.name, parent.name, parent_mean, a_prior, b_prior))\n",
    "\n",
    "        return a_prior, b_prior\n",
    "\n",
    "    def sample(self, w=0, t=0, silent=True):\n",
    "        \"\"\"\n",
    "        Семплируем из вершины\n",
    "        Параметры w и t нужны, чтобы не учитывать одни и те же данные из ребёнка и родителя \n",
    "        (см описание в тексте выше)\n",
    "\n",
    "        w: количество успеных исходов, которые мы не хотим учитывать при семплировании \n",
    "        t: общее количество экспериментов, которые мы не хотим учитывать при семплировании\n",
    "        silent: вывод логов, False если нужны логи\n",
    "        \"\"\"\n",
    "        a_prior, b_prior = self.sample_params_from_parent(silent)\n",
    "\n",
    "        a, b = self.beta_params()\n",
    "        a = a - w\n",
    "        b = b - (t - w)\n",
    "\n",
    "        a_post = a + a_prior\n",
    "        b_post = b + b_prior\n",
    "        \n",
    "        res = beta.rvs(a=a_post, b=b_post)\n",
    "\n",
    "        if not silent:\n",
    "            print('sampling %.4f from %s with α=%.3f, β=%.3f' % (res, self.name, a_post, b_post))\n",
    "\n",
    "        return res\n",
    "\n",
    "    def update(self, wins, trials):\n",
    "        \"\"\"\n",
    "        обноваляет статистику вершины и всех родителей\n",
    "\n",
    "        wins: количество успешных исходов\n",
    "        trials: общее количество исходов\n",
    "        \"\"\"\n",
    "        self.wins = self.wins + wins\n",
    "        self.trials = self.trials + trials\n",
    "\n",
    "        if self.parent is not None:\n",
    "            self.parent.update(wins, trials)\n",
    "\n",
    "    def beta_params(self):\n",
    "        \"\"\"\n",
    "        переводит wins и trials в alpha и beta для семплирования из Бета-распределения\n",
    "        \"\"\"\n",
    "        a = 1 + self.wins\n",
    "        b = 1 + (self.trials - self.wins)\n",
    "        return a, b\n",
    "\n",
    "    def no_data_in_parents(self):\n",
    "        \"\"\"\n",
    "        проверяем, есть ли у родителя данные, про которые мы не знаем.\n",
    "        если нет - то нам нет необходимости запрашивать у него информацию\n",
    "        \"\"\"\n",
    "        parent = self.parent\n",
    "        if parent is None:\n",
    "            return True\n",
    "\n",
    "        if parent.trials == self.trials:\n",
    "            return parent.no_data_in_parents()\n",
    "        else:\n",
    "            return False\n",
    "        \n",
    "    def total_trials(self):\n",
    "        \"\"\"\n",
    "        общее количество попыток в графе\n",
    "        \"\"\"\n",
    "        parent = self.parent\n",
    "        if parent is None:\n",
    "            return self.trials\n",
    "\n",
    "        return parent.total_trials()\n",
    "\n",
    "    def sample_multiple(self, size):\n",
    "        \"\"\"\n",
    "        делаем выборку размера size с текущими параметрами wins/trials и параметрами родителя\n",
    "        size: размер выборки\n",
    "        \"\"\"\n",
    "        sample = []\n",
    "\n",
    "        for i in range(size):\n",
    "            s = self.sample(silent=True)\n",
    "            sample.append(s)\n",
    "\n",
    "        return sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь давайте попробуем эту модель в действии. \n",
    "Для иллюстрации, конечно же, возьмем пример рекламы. Но немного упростим - опустим часть с аукционом и представим, что у нас есть возможность покупать рекламные показы небольшими пачками по 500-2000 штук за раз.\n",
    "\n",
    "Представим ситуацию: компания \"Horns & Hooves Ltd\" - рекламодатель, который рекламирует игру  \"Mushroom Farm\". Мы можем купить рекламный траффик из двух других приложений, пусть это будут Grindr и Fidget Spinner, назовём их `app1` и `app2`. Мы хотим оценить, как активно пользователи этих приложений кликают на нашу рекламу - то есть мы хотим посчитать CTR. \n",
    "\n",
    "Сначала мы хотим рекламировать наш апп в США. Пусть CTR в первом приложении в Штатах будет 0.06, а во втором - 0.07, но мы об этом не знаем и хотим эту вероятность выучить.\n",
    "\n",
    "Сделаем такую иерархию: сначала модель для всего рынка, потом для США, а потом для каждого приложения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "market = Node('market', downsample_size=200)\n",
    "\n",
    "us = Node('us', parent=market)\n",
    "app1_us = Node('app1', parent=us) # 0.06\n",
    "app2_us = Node('app2', parent=us) # 0.07"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для наших экспериментов напишем специальную функцию `simulate_traffic`, которая в качестве параметра берёт вершину и эмулирует определённое количество попыток с заданной вероятностью успеха. После этого функция нарисует красивые (я надеюсь) графики, по которым мы сможем понять, как модель себя вела. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def beta_std(a, b):\n",
    "    var = a * b / ((a + b) ** 2 * (a + b + 1))\n",
    "    return math.sqrt(var)\n",
    "\n",
    "def simulate_traffic(node, prob, trials, silent=True, seed=1):\n",
    "    np.random.seed(seed)\n",
    "    random.seed(seed)\n",
    "    samples = []\n",
    "    means = []\n",
    "    stds = []\n",
    "\n",
    "    for i in range(trials):\n",
    "        s = node.sample(silent=silent)\n",
    "        samples.append(s)\n",
    "\n",
    "        a, b = node.beta_params()\n",
    "        means.append(a / (a + b))\n",
    "\n",
    "        std = beta_std(a, b)\n",
    "        stds.append(std)\n",
    "\n",
    "        w = int(random.random() <= prob)\n",
    "        node.update(w, 1)\n",
    "\n",
    "    samples = pd.Series(samples)\n",
    "    means = np.array(means)\n",
    "    stds = np.array(stds)\n",
    "\n",
    "    plt.fill_between(np.arange(trials), means - 1.9 * stds, means + 1.9 * stds, alpha=0.05)\n",
    "    plt.plot(means, color='blue', alpha=0.5, )\n",
    "\n",
    "    plt.plot(samples, alpha=0.2, color='blue')\n",
    "    plt.plot(samples.rolling(10).mean(), color='black')\n",
    "    \n",
    "    plt.hlines(prob, 0, trials)\n",
    "\n",
    "    plt.ylim(0, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сейчас мы купили 1000 рекламных показов в `app1` и смотрим, что происходит:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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UahT/83++snQ8FgMKBceyYVkGTNNpQ+8nNlKu2t4zXWtjYkLEoxw7NmNLmFFsG8jnZ3oV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\n/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0WpXb5sLUOOU5/kr45iDKpiY5xlY1Gx0WqNFo+DYU0isCL/pZdOdh9lM2acJVnlJF89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\niqIoirJW/j/Yw9EMnEirZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efbaea20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_traffic(app1_us, 0.06, 1000, seed=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На этом графике у нас много информации:\n",
    "\n",
    "- вертикальная линия - это 0.06, реальный CTR, \n",
    "- синяя линия - мат.ожидание Бета-распределения на основе истории, $\\mu = \\alpha \\, / \\, (\\alpha + \\beta)$\n",
    "- фон вокруг синей линии - $\\mu \\pm 1.9 \\, \\sigma$, где $\\sigma$ - среднеквадратическое отклонение, а $\\mu$ - мат.ожидание\n",
    "- бледная гобуая линия - семплы из $\\theta \\sim \\text{beta}(\\alpha, \\beta)$\n",
    "- черная линия - скользящее среднее семплов\n",
    "\n",
    "\n",
    "Видно, что ближе к 1000-му показу мы достаточно точно приблизились к 0.06. Чтобы как-то приблизиться к 0.06, нам понадобилось около 500 показов. \n",
    "\n",
    "Теперь давайте покажем рекламу 500 раз в другом приложении, CTR которого немного выше:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6Ve2o+hmaFkNvr4ne3lJLCMMwlWkrYSEE0NkZrLDQdd1XBc56ilepYllcYnvo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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efb86908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_traffic(app2_us, 0.07, 500, seed=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Так как у нас родительская нода (`us`) знает, как вёло себя `app1`, мы можем воспользоваться этой информацией для предсказаний значений для `app2`. Видно, что модель сначала выдает предсказания в районе 0.06, на основе данных от родителя, а потом начинает ползти вверх.\n",
    "\n",
    "Давайте еще раз покажем рекламу 1000 раз в первом приложении:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vPvZSKSzc+4/HBQtqZjoDgYZ9YWVxMWzatGvLJRJJsLGH7Ujlo7UZt90VvRu32/yuTwBR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\nzJv3OLNmvcWAAdtp0sRLQcE4nn/+Mu69919ce60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NPT2dXHvtmXR2vsX3vncLkOITn/hr\nmKRplCmvbMAiYAiwbvpLgA2ATVcL0AC4HR2qAHtW82IgBtiJ1kNd4Z4GmoFpQAYIOp+POO940rm/\nDkgCM53rvwded36vB7qAJiduAeDXQI9zvRZ4GbAbLWx3nrMdsMO5RUAC2AzsBY52nlsHhIFqYC75\nxUXPAd8B3gcsA+YD7sbmRaDfCb8X2II5H8SvlU4578C5ZzpwrBPHp5w4PAvsBCLOs+O4HZ/yPA8s\ndX3f6TwvS+HCqHUU5gPAekweWI7GyLrT+ZsFZjnxne78X4PJlz8Btzr3rQGWO7897rwngpFhtXNP\nDUb+PwZOAc50nt/tvG8axii4G5O3zwHbMHliPwuA+5z3eNNi2Y0pm35sdt7XABzlxE0Bf3DeOZO8\nzNx5NIApzwAVmLJeCWzFlDnbAA4CUedZ1c73Hifuo/EaRr4ZTN63YGSyCSOfOKZeWJ4hf/5MyImD\n3z71tcAcTN2pduL+/zD1e4mTLvuOYizD5GcxtgBtzv/e9rUSk29+ZMm3ITY/12HyZAamfu/AlBu/\n/H4LcJ/M5Y7nECadsymU/w7nuX7PqieflxlM/fCmwabPLz6vAvNc3915BKbetDv/bwYaMeXJ8iKm\n7k8DXnKuO6Yf0hg5aEw5UZi2YzdQuE9Qntcw6e/G5P9STH6Hybev9lMB7AIexrR77mv9zjv+jGlv\nrG+HlXGjJw5DTvwLV+PleQlYiJFXl/O/lUPGSaf7eT3O9bcc2YBpY2sZzptOfKdh6kyQ4eUETNu/\niHxdBf+2owMjq+cxebDC552afPufQ5SNkXBbNtrbF/GRj5jCctNNz/Htb19CT08Hu3dv5/jjz+Nd\n7zqO6677EDU1jQwM9PH5z9/Oj370D7z00pPMmDGX448/j5/+9J8AuPnmF/j3f7+ShQtX85OffJmL\nL/4Ghx9+OsEgPPpoVU7DP+GEvbS0DOW012QyS3e3GWUmEpmC+Vc7InrxxQQ9PUFqa1O5UY2Xmpo0\nnZ0hduzYzO9+dxuf+tRFdHQ0MjAQYObMISorMwUjp8rKDLFYlh07wvT1hejuDhIIaLZujZBKBeno\nCLNgQR9HHtnNli0xurtDVFen2bYtwrZtUfr6grkRWjKZoa4uTTSapaoqk7PYvPxygpdfTlBdnSKV\nUgwMBJk+fYhzz32L3bvDBaOvWbMG6e0NsGfP8HnVBQv62bQpnpvmqK9Ps2fP8JFbe3t/Lo1Wm+/u\n3siGDS/T3LyAX//6P/iHf7iSVKqW3bvDaJ3X6uvrU6RSAbq7Tb6kUoqOjgF++ctvceaZn2L16gBb\nt0aJRjVtbQO+o9Cqqgy7dg3xs599jVNO+TuggZ6eIL29IXp6ggwMKA49tIdVq/bx8stxlBo+SrbP\ndafFS0NDit27h8sJyOU1wLZtEXp6THqiUTOCc4+awmFNKqWcOfiBnBXAjdeXwVo07Oi5psZY5l57\nrfDehoYU9fXpgjTYUbEdUVvLRkvLIMlklnTaWBgApk8foqamtCNI7ajcbdmYN6+fUIicFayuLj2i\nb8SmTTFSqXyAWMyMYK3FYObModzI35tn7lGkl0DAlF8ozFuAzs4gO3dGqK9P0dCQHrNlIxzWzJ07\nkJOjpVj9qKlJ092dt2zYkTuQk719JsDLL8eHTS21tg4WpNUri/5+U08AmpqGyGRUziphy4SNb2vr\nIB0dYXp7C0fd7pF4NKqpqUnnrKlgLF7btkUL/o9EjKXBluFio3mvlcnitti45ee2/rjvCQaNxWLz\n5sJyY5k3z9xjp5m2bs1bNoJBIwt3mmz77bZKjdQGeKmvT9PQUOjUMzSk2Lw5RmVlJleOvc+MxbJU\nV6fZuTOSi/Orr8YLpssts2cPEI1meeGFpyfVsjHlfTZmz57DrFlL+cxn/pPHHruLRYuW8fWv30Mw\nqLjyylMZGtpHb+8uQqEQ99yziYGBMJFIlGOPPZXnnvsjl112TE7RAKivr+WJJ37FE0+Y3UAPP/wE\nWlsX8/jjxrFr4UIzR7lqVSOzZ+e3h62sLO49f8gh5m8gYDLez+lt1iwzF1xTY+YrFy5czIknnlbg\npW7nvt2dRk2NmbOs9VGc6+vNfG1zs5mntvPlK1eaudM33jBpisXM/GZnp4nXjh35eenKSvPuJUtg\n0SKzR0JbGyxeDCtXtuQOzbKsWGGe7T5vwLJyJRx6aOG8vfucEDDPrq2F5Y6PVDptvPdrahazerX5\n7YQTzmTlSuOnYuPZ0mLmKOfMMe92ryoCeM97buVd7zINRCxm5nBbW4cfMgdmZUB3Nyxf/j+MxMqV\n+Xl2m8cWm0eHHFJ8p0B3+fEyb56ZIwaTxzY9waCZb3bvyGpXBcyaZfI87KO/hMOFjom2DNpyV1tr\n8iPq6Wvtqg93GubMMeUiEoGlS808+O7dZo+Riop8mK1b83Eqhb17zf3NzUb++/aRy7NSqa8v9JGx\nTpJWfvPn5+PozbPeXiMXP0KhfJl05y3kl8DOmGH8jWwc3P4jjY2mjFrC4fxGbtOnm/q5bZvxXYlE\nTP166y1TP2KxwhUIDQ2m7Lt9NtxpWbTIxDfm6I2LF5t65D56vL29MK1+srD32zx0vw9M+7Frl2kT\nt28f7oxqVwSCeVdDQ97fxqbZtgXLlpkDJxsajAxtGa6vNx8bd6s02/h669bcuebT32/q0J49Jp7B\noClLkG+H7f8rVphyvndv3q/E4i1/yWQ+TaFQ3veosdHcO3268deqr8/70R1ySOF9I2HLkJeWFvMO\neyint12x9TSVMrLT2sR75szhbfGiRRCLaVKpImcxlIkpr2xYTjvtY5xzzsfYt8/s1QBm06odO7ag\nlGLp0hUEgxU5pzUwqzdmz17Ma69t4LjjPsgjj9zBBz5QaP5vaWnn4YdNg9LcDMcfbzJzxQpT8G1n\n4Vfo3RswufEbmdXXm0Z7pAJZbERn393WRsFZIGAqhNcZzE04bNI1f75xrLJKk10G19hovNMXLjR7\nIpx2WuFhXO5GYcYMfwe9SMQ/7n6/Wac0W8Hd5814R+fudIVCpgEdCfu+5cvzz1+61CwPdON34FKx\nVQ77g+3YvUuuodBZ0P2/3dnWjY3XSJ2y9x6bPhuHUKj0Tt0+a/jqieFhxyuz1lbT6I/1/IaWFlMW\nN27Md3DuI7fHIiM3I1lT3AcRgol7U5Mps7t3G6XBe78t19Onm3rjfkcymT9jCIyyuWMHuVFqJFIo\nV6+CVFFR+D0aHa5EjudcjJFk4Ocn09Ji4t3ZaRRk9/3e97vbVO9Gi8mkSXMsZvLSfd07cAsECpW6\nxkajbLjltWyZkf9zzxX+Xls7/Oyi0bb0ttfjcfNeG5d02pRDG9cFC0xZ8B5v71UGip2CbZ2aly4d\nHqdlrhkg2x4rZRSQdHq4sjHZB7BZpryy4a5o7nNQXnoJ4vHZrF//U9av/x3ve98l3Hprfj18XR00\nNyvWrv1HHn74B1x88ZcLNmSxKJUknTba/XHHuX83f+vqTObZQtrWZuIxksd8sQJsTmk0Db9f5bX3\nLVli3meVGfeIw45U3YxWuAKBfGOUSBhlIxw2FdU94vEbMdsOPxjMX6+qMsqK1eyXLPF/bykKiPvc\nFeOklU+vOz5+aZwzxyhvdqRiw3iVFDfhsHnPSMrG3LnDG3Qv1uI0Ejb+gYAZQT37rH96vHKfZAMS\nBAAAHU9JREFUSGUjHDYyrago/awE+6zxds6j3WP3cGgpzVd12DPcCpSXYLD4ctqR4jxWJcXmWWXl\n8IMHIZ9nNTX591rLk2077O82HeGwKXvJZL4DaW3Nr/QZDbu6pVic/eI3Em55eU31Vs7uJeHuM1NG\nWvLsjpuNx1LH1Wvv3sIj4RctMgM+u/LC77kzZxbWV7tXiPv5fmny+z7aNZvvmYzJKzcNDSbu7qMJ\n6uryeWlW1RV/H1AwWC4ljn7ymOwzUSxTXtkIBs02vL29ZjRhzf5PPAEdHcZRSqkAtbWns8Dxm9q7\n12xc8/LL0N9/NsuXn82GDfZQL81ZZz3FL36xinC4kt/+1hRWa8I3z8v/P3u2+WvNfJWVxS0JtmBH\no/nRVn19fkmZVTai0cKD06LRQotHNOp/qqJS5nlW2UgmTQX3W+HkPUgtGMybVt2V2Z1W79HxkK9c\n7kpgl6PV1pqKVaxwV1WR2xPANv7eRtCtbEDe8uF+t/c+t9wCAYoeAueH7ahiHrcHdxrC4Xwljkb9\np7DcjWwxIpF8Z+FtFNzpsctIbb56ZRQMmvLg3u/Bm0/e59v0BAL56ZpS8Vo2KivNqM2dH1bRGk3h\ncmNlX2wqo1RsvGyZ9I6oFy70Xx7rTpdbfq2theWu2PvGcs29ksQb1psf7o7Rq+TaHT5LoaUlXxfs\ne+NxM0DyMtZVkfF4YZu0zMff0m1dsWmdNSvf/nmvwfByXFs7vL75HQrpZvr04vH2Mt5Rv41DKGSe\n0djoH86rlLnzzvZPY2WsSr9YNsbJs8+aec36ejOCWL/eFPrGRjjrrI+yceNRRKPtNDSYaYA9e/Km\nqqoqY27ds8dYCi65pIPu7hCHHprkvvtiXH31P/OhD5kK7p2e8GILW7ERpDtMfX3+1NfGxuGbWHkb\nD9vxua0d7ufW1JhGxNuwJ5PGMuE2z7pNyhb73mINjNsfxVt4YzHTePvdO1IDbe9dudJsg2yVjWIj\nC7+j3kdTNvwsFH60tRkFtKursMNbvjw/xeJVuizFrDal0lBkMYp3GqW+3uR/f39eSQMj+7feMuXJ\ndiDLlxsZuKeH3Aqre1prPA2Pvcd2fDU1heXMvq/YLp/FiMfH7qNRLH4LFuTL5MyZpkOzCpndS8Lv\nPhg+v+7No7Y2/w5+JGuAtxz6WaOam8277G/eNqWYpWY8BAJGLnV1/hbLQCBvJS3FyjFnjpGv3fTK\nT7525O6eVrI+GW5GUjb88Po0jQWvBXqk9tsPv+sr/BaBOFhlo6Ulb63dX0p9hvXtEsvGONm+3TRS\np55qlImtW40CUlUFlZVBDj+8nblzCx2Tnn/ejLiTSTNfap18Vq+uyW3C9cAD/TQ3581aoykb1dWm\nQ3QX1mXLimuWiYQJ7zePaRsVW9Fqa/NbPVvc98Vieec173vc4ebNG366qPdZfsydO/LBZGMZvY6H\nUvwlik3JlNKZ1taa9HV1FVo0QiHTEEYihU6H+9sZNjaOPnIcbYS2dKmJs91Yzh0v+3fFCmPBczs+\nWse87m7z+0jyKXYtEDBKltuaNVEN2P7K1uKuK6GQ/0jbSyhklJRo1Dj5+Snm4G/JGi/u9AaD/uVC\nqfz0iZdSrRqWhQvz94w24rdxK1YObJmyo3k/3xAv9t0TObq2U5a9vWMrP9ZHxI9IZPS2Uqm8DMZq\njStm+RgPY53+FGVjnNgDlNyj9+bmwjDF5rzdBdMvI9wVORDI7+bm54/R1DR8vs37XveIe8aMvNOT\nxT2P7n1OKY2lFz9zu60U7s57tArqnuMsJ4sW+f9eyujGz7LhVbZGwlpWvI2GtTr19RllBPa/Qyzm\ni3DIIUY56OkZXd7ujr6qyigPflMx7noxbVq+kauq8h+BKZUf2RdrEJXynzt+O2CVlIULzUoJ73Sa\nH4mEkYmfEuJdweFlpPLpvreYD9hY6+VYBgY1NWaa2HtQnqWuzlgv/SwjxRhNHhZrVSzVwdhOTY9F\nHn5hreI+c6b/9GJdXeGqw3h8uFVvJMa6/f5EMGOGiZ/d9dRvOnwymPLKhjWLWkqZo/IzIXvDzJpV\nWMnssinv9uQjvacYgYBRZLwjC6+yUYpZdqQwI8XHNqrTp+//HPlEMZZGy4tfWkudRgGT111dxRvj\ntjbjkLtvX/kUL6XGN/JrbDTm99FWTHiVcD+8SyDfySxbVlo+BIPlkdvBsAVSMUXDMtY6W11tpr1H\ns+xZxblUK1Jr68RYC9wniPsNKurqTJzch2GOxVKwYIG/8/94KHWFnF1Km81OrEVlrEx5ZaMU7+FS\nlA3vfd5KZq9PhJm3WAMWi5kRaimFd3/DJJNjn1N3M9Jqm7HiPpfBj1IqlZ9lY6Rnekkk8h7vxZ5v\np77Gy2hLc8EoucX8OEaiWDpLHUmOhYma6jjY2R/ld3/RWjt5pw6Y2bscxOOltTt26Wap2Pq5v9iB\n10gWLZsf48mXYNC//vjtrTEabl+VUggERl9FV07GpWwopS4FrsTspbse+KTW+okRwr8X+CZmD9qt\nwHVa6/9yXb8A+CFmL1WbhQNa61GLz0QrG7W1ZgRYzgpeTNloaDBLuEoxdU6UQjIe9kdJ8aOlxZgs\ni3VidhOekTpht0yTybwFYiJlUGy0Mxrt7fmjuEfDHrI00UyUHCY674ufwKzJZrMEAgHf6+VmrO/X\nWjM4OIhSCqVU7r5sNgAU3p/JZJg+XdPbq8hmTViAoaEh7I7OmcwQg4PK+UB/vwLyz507N0AoVHi/\nsP9UV5vpxckUqbdOZbNZ0ul0QTmyHzezZxuLzngYGBiY9FUpY1Y2lFLnYBSHv8FsQH8FcL9SaqHW\nerdP+DbgXuC7wHmYwyl+oJTarrV+wBXUbjxvJTomI6JtyPdX2VCq/COaYpkcjZq5SmvKO1Bm1JE2\nJJsIrFe0xe59UgybNyPtu+CWaVNTfv+TiRyFu3dAHAuJxMSMut5upNNphobMBLZSAbTON67p9FBu\nm3LjtW86baUCBY2wWxkYGBgY1tm7G+tiZDIZBgcHnDDmnnQ65WwDb+KgtcrFwf/d/USjmlAoQCaT\nJZs18U6nzeGJqZRRGIwDeiY39TU0RM6CEQhoIhETJhYLMG1alL4+TV1dllhMO89Nk81qEglj+Uil\nbHuhnE9gmAyMPNNks+kCGXvDvNOVlmw268ihNOXWr58opjyX+v7BwQG0zhCNmnzNZGz5y5cTWxZt\nvmUyZsuGTCbltJVqWD7bj1FkUoRCWeLxyTXdjceycQVwk9b6VgCl1MeB04ELget9wn8C2KS1vsr5\nvlEpdYzzHLeyobXWY9gRwaCU2Y7XvXOal2J1yG+N+2TUt/EspxpPmPEykVMkfixcOLZ5y6Ymswtg\nqWlWauSNncbLaLuxHswcLKb4TCaTG7WlUkNUVgYIh8M5S4JpDLNEIopEwtiys9lswfVMJksmk+9s\nrUISi0EoFCSb1aTT2YLrpqEuVFhsBzs4OOAcUx7MdeiRCMTjMezeO+44ZDKmw89kNNksjnIAyWSM\nsNMQmWkQTXV1lmRSU1WVBbRjuQgRi8UKnmstGhGX521FhamLfj5V9h5v3PJxzMvILrGsqAjmOhy3\njGwaiiktVk6ZTMbp0NQwOY42Cj/Y6e/vJxBIuzr2vHLpl8Y5cxTJpGJgwIyarFzzh1mqgo9fx2+V\nwIyzHlbrNLEYxGKRXDlw57O3vNh8tJ9YLEAkUliX3Nft4LWiIkAkEisoa5PBmJpOpVQYWAV8xf6m\ntdZKqQeBI4vcdgTwoOe3+4EbPL9VKKW2YFqEdcDntNYvMApK+a/oADMd4jf3Nppl40BTivPnSPG0\n56scrIy1025sLO7YFAiMvCwXTDk4GJztDiQHolxbpcI20ul0msHBfqfzVIRCmng8Me4RtbeDDQaD\nBF0jCL+O2IwACzvbWAwSiUTBvaW+3z3d4k6HO93FdoUsxZpQzHnb3aGPFG93R+UXzq8T83ZWVk5G\nYQkQCoWGdWaZjC4YhbutUbbD9na4kzFFZtM1NDTk6eRTKJXFWAHMEfWVlVECgUDRTt1tsYrHjdUh\nHDZKqpVDNBomGAwWyNJtkbKdvlXwlIJkMoDWEAiEcgquZSLlY+NzoCxYYx2nNWDOwd3p+X0n+fOI\nvTQVCV+llIpqrQeBjRjLyLOYM3T/HviTUmqJ1trnSK88IzkVFq/k5u/BqmyMBb9OtK1t0qNxwJg9\nu3AbZD9G2wL4nYC7XLsbXr9pBq01qVSqYLrAzm5ms9nc/cWmKgYHBx2TdDq3zM4qhBUVikRi/ApG\nYZrUiB3taNdtWm3Y8bz/YJ9+GM3KUGoaRuuoRhqBa61JpzO5DlfrwumBYtaU0awlmUwmN23hTUMq\nlWJoaJBg0ORvPG6uW+UpFlPEYpGc5UopVdJI35tOr5JZCm4ZlVJGJ4oDbXE6KIzCWuvHgMfsd6XU\no8AG4P8AXxrp3muuuYK6urzdP52GI45Yy8knry16j59iMdWUjZHiOVXSMBHU1JR+NsTBhG1oxlr5\n/RSBUp6hlDEVZ7NZwuEsylnh4/ZJsA1+JpMhGs2PwFIp43cAir6+DPG4NRvr3LyyNcHbUWIspgiH\nQ0Sj0YLOJxQKHVSd81Qz9x8oSlVaSqGYJcVvasDrs2CnN7JZTTCYJRgkZ23I+zSYMphIKGKxKEop\nQqHQhOT1RHTYB0JJve2227jtttsKfuuyGwdNEmNVNnYDGcC799x0YEeRe3YUCd/tWDWGobVOK6We\nBuaPFqFrr72Bo446NPe9t7fwKGU/mpqMY5bblD+ZPhvvFMzcccYzQh6O1/P67UQ6nSaVGsI9b5vJ\nZFDKzO1aXwK3Q5cdLXllls1m6evrIxYrVAT8/BHy7zLP7u/vIxrNEo0GCYWiRCKRovP92ayZ+w2F\nQrnfjjlGo7WZLgiHw7nRmN/9gUBg2ChxskZvwsFPqaN5rxXBq6QEAqFh5dhtcQgfyLXLBxlr165l\n7drCAfi6detYtWrVpMVhTMqG1jqllHoKOBG4G0CZ3uFE4F+L3PYocKrnt5Od331RZrJvOXDfWOJn\n7i3860cikd+tcsECs5+/nY4oZ19XXZ3fhdLLkLM3bt4sN7LWY/ug0Tbd2R/Gs4JiaGgop2CkUinH\ni95tSs93rNbpLBBIo5TtOPPe1n6dr1sZSaVSBfPlo40W3CbzgYF+5/vwzn0soxc7ZeC9P5vNkkoN\n5OQYDAbJZNJkMlnHzyhIJBIZ5vyYTmcLRnR5p70A6XSGRAIqKuK5eWF7XzEHynTarISIRLIkk9EC\nJaCURt+mqZiPjZW3KBPCRFNqPTzYp7IEw3imUb4F3OIoHXbpawK4BUAp9VVgptb6Aif894FLlVJf\nB/4To5h8EDjNPlAp9UXMNMorQA1wFTAL+MFokfH6LNgy5z1drxgVFeZjz74op7LhPXLYYtbXDxIK\nFZqtq6uVc95KwOcz8XseuBnp3ACLnQro7+91zPIKpbLE4wrIEgppkskYwWBwWIeYX0uuicWCBeZ2\nGzadThesKnB3vOavWTXgngO2Co13lG9XHQQCxskrHIZ4POSYa9M+qxf8lZ68X4JZshkMGnOt1lZJ\n0DmzbiKhiETChMPhgsawlOVxfhYDrRXhsLE4wOiNbDabpaZGEwxqqqrI3ScIgjDZjLn10Vr/j1Kq\nAfgyZjrkGeB9rmWrTUCrK/wWpdTpmNUnlwNvABdprd0rVGqBf3fu3Qs8BRyptX5xtPh4VyJEozij\nv7Gla6zTKGln7aafg9Cgs4mEd2QOpqMZGBjIXTdpGCIeV1RWVuQ6lve8Jwtk0TrrLDlLk8noXKeb\nX2sd8B2Ze+PqtQCM1tmNJAfr3a31EFobmcfjEceEGSAWiw17/kiOZaPFxW8En8lkgSCJRDxnSfB2\n0GaEn815ykcikEhEcun3mln93mOVHq8iYZeoAURdp0+5zb3BYNA3baWM1ibCYhAIBFiwwKxMEj1D\nEIQDybiaIK31dzGbdPld+5jPb7/DLJkt9ry/A/5uPHHxLg1TqrRtofcHYyLvJxRyj7jN1IdxgssQ\nDqtc55R3oAuQyWhiMU00aszqdk+BioqkE381bAmfxWsZcFsICpee5Uf/ZqpiKLdJjNdC4B39F/Ob\nSKVSgOnABgb6HQcsMzdvHbDGQ6lm0mIysYzmFZ51tNKRwoz2HrcCUux9B9sKhXD4wJ6HIAiCAAfJ\napT9YaJHbKP1fXY1QDSqqKxM+EwNaILBEImE0YLc19wOdN7R8P52usVG/5lMClBUVCQKLADFRv+F\nDoduxSNFKGQUp2gUksko4XB4yjh0TsZSS0EQBMGfKa9sTCapVIp0egClIBoNl2TqLmUd9kQtyRpt\n9A+MGMZPMTJTOJpgMEAymchNE0inKwiCIJSKKBslYlYvpInHzdrtt6Oz3WQpRoIgCMI7i7dfjzkC\nZn8D/93o3KtavLsKmtMc01RUmE2KDpb5eEEQBEGYCrxtlQ17wI0drRtfi/7cWRre1RzpdACtjVPl\nwEAfSmVzyx8hS0VFgHixgwoEQRAEQSjK20LZMLs0DmL3VjAbSg0Sj1OwGiQahYqKhO9qDrMBkmJw\nMEtVFSSTkZxDpV3OKQiCIAjC2JnyysbgYD/9/f1UVEAkEiaTMcpDKASVlUnn8J1swT4Tfs6NAwOa\nzs4sNTVZKiuRrW4FQRAEYYKY8spGMhmgtjZUsLOil1IcH0Mhs5ojGg0ieoYgCIIgTBxTXtmIRqMT\n4ktRV2f22JiKJ4gKgiAIwsGMLKtwUKq8h5oJgiAIwjsVUTYEQRAEQSgromwIgiAIglBWRNkQBEEQ\nBKGsiLIhCIIgCEJZEWVDEARBEISyIsqGIAiCIAhlRZQNQRAEQRDKiigbgiAIgiCUFVE2BEEQBEEo\nK6JsCIIgCIJQVkTZEARBEAShrIiyIQiCIAhCWRFlQxAEQRCEsiLKhiAIgiAIZUWUDUEQBEEQyooo\nG4IgCIIglBVRNgRBEARBKCuibAiCIAiCUFZE2RAEQRAEoayIsiEIgiAIQlkRZUMQBEEQhLIiyoYg\nCIIgCGVFlA1BEARBEMqKKBuCIAiCIJQVUTYEQRAEQSgromwIgiAIglBWRNkQBEEQBKGsiLIhCIIg\nCEJZEWVDEARBEISyIsqGIAiCIAhlRZQNQRAEQRDKiigbgiAIgiCUFVE2BEEQBEEoK6JsCIIgCIJQ\nVkTZEARBEAShrIiyIQiCIAhCWRFlQxAEQRCEsiLKhiAIgiAIZUWUDUEQBEEQyoooG4IgCIIglBVR\nNgRBEARBKCuibAiCIAiCUFZE2RAEQRAEoayIsiEIgiAIQlkRZUMQBEEQhLIiyoYgCIIgCGVFlA1B\nEARBEMqKKBuCIAiCIJQVUTYEQRAEQSgromwIgiAIglBWRNkQBEEQBKGsiLIhCIIgCEJZEWVDEARB\nEISyIsqGIAiCIAhlRZQNQRAEQRDKiigbwpi47bbbDnQU3nGIzCcfkfnkIzJ/ezMuZUMpdalSarNS\nql8p9ZhS6rBRwr9XKfWUUmpAKfWSUuoCnzB/pZTa4DxzvVLq1PHETSgv0iBMPiLzyUdkPvmIzN/e\njFnZUEqdA3wT+BKwElgP3K+UaigSvg24F3gIWAHcCPxAKXWSK8xRwE+Bm4FDgF8Cdymllow1foIg\nCIIgHFyMx7JxBXCT1vpWrfWLwMeBPuDCIuE/AWzSWl+ltd6otf4OcIfzHMvlwP9qrb/lhPkHYB1w\n2TjiJwiCIAjCQcSYlA2lVBhYhbFSAKC11sCDwJFFbjvCue7mfk/4I0sIIwiCIAjCFCQ0xvANQBDY\n6fl9J9Be5J6mIuGrlFJRrfXgCGGaRohLDGDDhg0lRFuYKLq6uli3bt2BjsY7CpH55CMyn3xE5pOL\nq++MTcb7xqpsHEy0AZx//vkHOBrvPFatWnWgo/COQ2Q++YjMJx+R+QGhDfhTuV8yVmVjN5ABpnt+\nnw7sKHLPjiLhux2rxkhhij0TzDTLh4EtwMCIsRYEQRAEwU0Mo2jcPxkvG5OyobVOKaWeAk4E7gZQ\nSinn+78Wue1RwLuM9WTnd3cY7zNO8oTxxmUPZgWLIAiCIAhjp+wWDct4VqN8C/hrpdRHlVKLgO8D\nCeAWAKXUV5VS/+UK/31grlLq60qpdqXUJcAHnedYbgROUUr9nRPmGowj6r+NI36CIAiCIBxEjNln\nQ2v9P86eGl/GTHU8A7xPa73LCdIEtLrCb1FKnQ7cgFni+gZwkdb6QVeYR5VS5wHXOZ+XgTO01i+M\nL1mCIAiCIBwsKLNyVRAEQRAEoTzI2SiCIAiCIJQVUTYEQRAEQSgrU1LZGOtBcII/SqmrlVJ/Vkp1\nK6V2KqV+oZRa6BPuy0qp7UqpPqXUA0qp+Z7rUaXUd5RSu5VS+5RSdyilpk1eSqYuSqnPKqWySqlv\neX4XmU8gSqmZSqkfOfLqcw57PNQTRmQ+QSilAkqpf1RKbXLk+YpS6gs+4UTm40Qp9R6l1N1KqW1O\nG/KXPmH2W75KqVql1E+UUl1Kqb1KqR8opZJjje+UUzbGehCcMCLvAb4NHA6sAcLA/1VKxW0ApdRn\nMGfU/A3wbqAXI++I6zn/ApwOnA0cC8wE7pyMBExlHCX5bzBl2P27yHwCUUrVAH8EBoH3AYuBTwN7\nXWFE5hPLZ4H/A1wCLAKuAq5SSuXOuxKZ7zdJzAKNS4BhzpcTKN+fYurMiU7YY4GbxhxbrfWU+gCP\nATe6vivMCperDnTcpvoHsx19FjjG9dt24ArX9yqgH/iQ6/sgcJYrTLvznHcf6DQdrB+gAtgInAD8\nBviWyLxssv4a8MgoYUTmEyvze4CbPb/dAdwqMi+LvLPAX3p+22/5YpSMLLDSFeZ9QBpoGkscp5Rl\nY5wHwQmlU4PRkDsAlFJzMEuZ3fLuBh4nL+/VmCXU7jAbga1InozEd4B7tNYPu38UmZeF9wNPKqX+\nx5kuXKeUutheFJmXhT8BJyqlFgAopVYARwO/cr6LzMvIBMr3CGCv1vpp1+MfxPQTh48lTlPtbJTx\nHAQnlIBSSmFMan/Q+f1NmjCFaqRD8qYDQ05BLhZGcKGUOhc4BFPZvYjMJ565wCcw06/XYUzK/6qU\nGtRa/wiReTn4Gmbk/KJSKoOZsv+81vq/nesi8/IyUfJtAt5yX9RaZ5RSHYwxD6aasiGUj+8CSzCj\nD6FMKKVaMErdGq116kDH5x1CAPiz1vqLzvf1SqllwMeBHx24aL2tOQc4DzgXeAGjXN+olNruKHjC\nO4wpNY3C+A6CE0ZBKfVvwGnAe7XWb7ou7cD4xIwk7x1ARClVNUIYIc8qoBFYp5RKKaVSwHHA3yql\nhjCjCpH5xPImsMHz2wZglvO/lPOJ53rga1rr27XWz2utf4LZRfpq57rIvLxMlHx3AN7VKUGgjjHm\nwZRSNpyRoD0IDig4CG7SDpR5O+EoGmcAx2utt7qvaa03YwqUW95VmLk6K++nMM5C7jDtmIa86EF6\n72AeBJZjRnornM+TwI+BFVrrTYjMJ5o/MnyatR14DaScl4kEZmDoJovT54jMy8sEyvdRoEYptdL1\n+BMxiszjY43UlPoAHwL6gI9illTdBOwBGg903KbaBzN1shezBHa66xNzhbnKke/7MZ3kXZizayKe\n52wG3osZuf8R+P2BTt9U+TB8NYrIfGLluxrjdX81MA9j3t8HnCsyL5vMf4hxNDwNmA2chZn7/4rI\nfMJknMQMVg7BKHKfcr63TqR8MU69TwKHYabZNwI/GnN8D7TAxinkS4AtmGU8jwKrD3ScpuLHKaAZ\nn89HPeGuwSyj6gPuB+Z7rkcx+3Xsdhrx24FpBzp9U+UDPOxWNkTmZZHxacCzjjyfBy70CSMynzh5\nJzEne2/G7O/wMnAtEBKZT5iMjyvShv/nRMoXs0rxx0AXZnB6M5AYa3zlIDZBEARBEMrKlPLZEARB\nEARh6iHKhiAIgiAIZUWUDUEQBEEQyoooG4IgCIIglBVRNgRBEARBKCuibAiCIAiCUFZE2RAEQRAE\noayIsiEIgiAIQlkRZUMQBEEQhLIiyoYgCIIgCGVFlA1BEARBEMrK/wdfb68vMQTdYgAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efbb9400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_traffic(app1_us, 0.06, 1000, seed=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Траффик из второго приложения не сильно изменил поведение модели для первого приложения. Так же видно, что не смотря на то, что центр распределения (который $\\mu$) уже сошелся около настоящего значения в 0.06, модель продолжает \"эксперементировать\", выдавая разные значения вокруг центра. \n",
    "\n",
    "Давайте посмотрим, какие значения выдаёт модель при зафиксированных параметрах:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lWgs5Oc7WIiLdgwY4Sre3eXM8o0Y5vyV1e/Xs6R+MqRkRIhIuAf16NMbcZ4xp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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efaba898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(app1_us.sample_multiple(100), label='app1')\n",
    "sns.distplot(app2_us.sample_multiple(100), label='app2')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Так как в `app1` показов было больше, чем в `app2`, то модель для этого приложения более уверена в предсказаниях (дисперсия ниже).\n",
    "\n",
    "Теперь давайте представим, что мы решили запустить рекламу в России:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ru = Node('ru', parent=market)\n",
    "app1_ru = Node('app1', parent=ru) # 0.03\n",
    "app2_ru = Node('app2', parent=ru) # 0.02"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Допустим, CTR в России ниже, чем в Америке: 0.03 и 0.02 соотвественно. Но пока мы об этом не знаем. Посмотрим, какие значения предложит наша модель для нового рынка:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.076369207547950693"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VFVBU5KdLbtnnl/jS02HUKPj447ArEUlNgYWF+sGO/8L3KkwJqh0R8YqK/EqH48eHXUkw\nRo2CpUthvfooRWIukKmTDYJCf+CAlvQqTJ06ldxGu90UFBRQUFAQRIkiSWfmTNh5Z+jePexKgjFy\npO8x+c9/Ene/C5H2KCwspLDRvu0lJSUxaTvqYaFBUBgETHDOrWvJ86ZNm0ZeXl60yxFJCatXw+LF\n8D//E3YlwcnJgcGD/a0IhQVJRU39AV1UVER+fn7gbbdlnYVsYAiw6a7oIDMbA6wFvgUex0+fPALo\naGa9689b65yrbn/JItLYrFl+AGCy5+1Ro/zGUtXV0LFj2NWIpI62jFkYC8wD5uLHI9wAFOHXVtge\nOBLoh1+LYQU+QKwAkvROqki46ur8Qkxjx0JGRtjVBGv0aD8uY+HCsCsRSS1tWWdhBpFDRgLvcSeS\neBYtguLixNs0qi222w569ID58+FHPwq7GpHUoX/YRRLczJnQuzcMGhR2JcEz87ci5s/Xao4isaSw\nIJLAysv9lMnx45NvbYXmjB7te1JWrAi7EpHUobAgksDmzoWaGthjj7AriZ2ddvIbZc2fH3YlIqlD\nYUEkgc2cCcOHQ7duYVcSOx07+uWfFRZEYkdhQSRBrV6dxpIlqTGwsbGRI+GLL7TNtEisKCyIJKg5\nczLp3Nlv35xqRo70U0YXLAi7EpHUoLAgkoDq6owPPujEbrsl/9oKTenZ088A+fTTsCsRSQ0KCyIJ\n6Kuv+lJS0iElb0FsMnIkfPKJplCKxILCgkgC+vjjnendu4YBA8KuJDwjRsDatbByZdiViCQ/hQWR\nBLN+vbFo0QDGjq1MmbUVmrLTTpCe7nehFJFgKSyIJJjHH+9EbW0aY8dWhF1KqDp1gqFDNW5BJBYU\nFkQSzIMPZjJ06Nd06aKb9SNH+r0xqqrCrkQkuSksiCSQoiL4z3/S2WWXz8IuJS6MHOm3q168OOxK\nRJKbwoJIArnrLujTp5ZBg5aFXUpc2G476NrVz4oQkeAoLIgkiLIy+Oc/oaCgkrQ03YIAv3nWyJEa\ntyASNIUFkQTx+ONQUgKTJqX2wMbGRo6Eb7/10yhFJBgKCyIJ4u674YADYMCAurBLiSvDhvkeBt2K\nEAmOwoJIAli8GGbMgDPOCLuS+JOdDYMG6VaESJAUFkQSwD/+4behPuaYsCuJTyNG+E2lamvDrkQk\nOSksiMS5mhq491446STIzAy7mvg0cqTfrvrLL8OuRCQ5KSyIxLkXXoDvvoMzzwy7kvi1447+doTG\nLYgEQ2FBJM7dfTfk58OYMWFXEr/S0vytCIUFkWAoLIjEsW+/heefV69CS4wYAUuXwvffh12JSPJR\nWBCJY/fdBxkZUFAQdiXxb+RIcM4PdBSR6Gp1WDCzfczsGTNbbmZ1ZnZUE+dcYWYrzKzMzF41syHR\nKVckddTV+VsQxx0HublhVxP/cnOhXz/dihAJQlt6FrKBD4EpwA/WnDWzi4HzgbOB3YGNwMtmltGO\nOkVSzhtvwOefw1lnhV1J4hgxwq+34LQatkhUtTosOOdecs79wTn3NGBNnHIB8Cfn3HPOuf8ApwB9\ngaPbV6pIarntNhg1CvbaK+xKEseIEbBhAyxfHnYlIsklqmMWzGwg0Ad4fdMx59wGYDYwPpptiSSz\nZcvg6adhyhS/lLG0zJAh0LGjxi2IRFu0Bzj2wd+aWNno+Mr6r4lIC9x5p1834KSTwq4ksXTsCEOH\naulnkWhLD7uATaZOnUpuo1FcBQUFFGgYuKSYqir4+9/h1FNhm23CribxjBjhe2WqqvxMEpFkUVhY\nSGFh4RbHSkpKYtJ2tMPCd/hxDL3ZsnehNzAv0hOnTZtGXl5elMsRSTxPPgkrV8K554ZdSWIaMQIe\ne8wPDh0xIuxqRKKnqT+gi4qKyM/PD7ztqN6GcM59iQ8MB246ZmZdgHHAzGi2JZKsbrsN9t9f/9C1\nVd++fhqlbkWIRE+rexbMLBsYwuaZEIPMbAyw1jn3DfBX4DIz+xz4CvgTsAx4OioViySxjz+Gt9+G\nRx8Nu5LEZbZ5F0oRiY623IYYC7yJH8jogBvqj98HnO6cu9bMsoA7ga7AO8BhzrmqKNQrktSmTYP+\n/WHixLArSWzDh8OsWVBSogWtRKKh1WHBOTeDrdy+cM5dDlzetpJEUtPKlfDPf8Kf/wzpcTP0ODEN\nH+4/LlgAe+wRbi0iyUB7Q4jEidtv91P/tGlU+3Xp4ntodCtCJDoUFkTiQEWFH9h42mnQrVvY1SSH\n4cO19LNItCgsiMSBwkJYswYuuCDsSpKHln4WiR6FBZGQOecHNh5xhF99UKJj09LPmkIp0n4KCyIh\ne/VVmD8fLrww7EqSy6alnzVuQaT9FBZEQnb11bDbbjBhQtiVJJ8RI2DxYr/0s4i0ncKCSIhmz4Y3\n34RLLtHukkEYMQKqq/3SzyLSdgoLIiG6+mrYeWc4+uiwK0lOWvpZJDq09ItISD79FJ56Cv7xD0hT\nbA+Eln4WiQ79ihIJybXXQr9+cNJJYVeS3IYPh2XL/NLPItI2CgsiIfj6a3joIfj1ryEjI+xqklvD\npZ9FpG0UFkRCcOWV0LWrlnaOBS39LNJ+CgsiMfbVV36cwm9/Czk5YVeTGrT0s0j7KCyIxNhf/gLd\nu8OUKWFXkjq09LNI+ygsiMTQl1/CvffCxRdDdnbY1aQOLf0s0j4KCyIx9Oc/Q48eMHly2JWklk1L\nPyssiLSNwoJIjCxZAvfd51drzMoKu5rUM2KEX8lRSz+LtJ7CgkiMXHYZ9OkD55wTdiWpSUs/i7Sd\nwoJIDBQVwcMPw+WXQ+fOYVeTmrT0s0jbKSyIxMAll8CwYXDaaWFXkrq09LNI22lvCJGAvfYavPoq\nPPEEpOsnLlTDh8OsWbBhg7b4FGkN9SyIBKiuzvcq7LGHdpaMB5uWfl60SGtsi7SG/s4RCdAjj8Dc\nuTBjhu8Gl3BtWvp50aKODBwYdjUiiSPqYcHM0oA/AicBfYAVwL3OuT9Huy2RligtLaWioiImbWVm\nZpJTv4bzxo1+Seejj4Z9941J89IC/lZEBgcfHHYlIokjiJ6FS4BzgFOAT4GxwL1mtt45d0sA7Yk0\nq7S0lOnTH6W4uCYm7fXokc7ZZx9PTk4O11wDq1fDDTfEpGlpoZEj4ZVX0li5skfYpYgkjCDCwnjg\naefcS/WfLzWzScDuAbQlElFFRQXFxTV07nwAWVldA22rrGw9xcVvUFFRwZo1OVx3nd+CetCgQJuV\nVhoyBDp1qmPJkh3CLkUkYQQRFmYCZ5nZUOfcYjMbA+wFTA2gLZEWycrqSk5Oz8DbKS/3H3/zG79Z\n1KWXBt6ktFJ6OgwdWs2SJf3DLkUkYQQxG+Jq4BHgMzOrAuYCf3XOPRxAWyJx59//7sjjj8O112oL\n6ng1bFgVy5f3Yv16jToVaYkgwsIJwCTgRGBX4FTgIjM7OYC2ROJKXZ3xu99ls+eeMGlS2NVIc4YN\nq8a5NN58s2PYpYgkhCBuQ1wLXOWc+1f955+Y2QDgUuCB5p40depUcnNztzhWUFBAQUFBACWKBKOo\naDiffdaBOXM0VTKedetWx7bbruX117M466ywqxFpmcLCQgoLC7c4VlJSEpO2gwgLWUBto2N1bKUX\nY9q0aeTl5QVQjkhsbNxovP32WCZNqiQ/PzPscmQrBg/+hjfeGEVdHaRpeTpJAE39AV1UVER+fn7g\nbQfxI/IscJmZHW5mO5rZRPzgxicCaEskbrz0UhbOpfG7320MuxRpgUGDlrJ6dRoffhh2JSLxL4iw\ncD7wGHArfp2Fa4HbgT8E0JZIXFi+HGbNymTvvefSq5cLuxxpgf79V5KTU8cLL4RdiUj8i3pYcM5t\ndM79yjk30DmX7Zwb6pz7P+dcbFbFEYkx5/yyzj171jJ27CdhlyMt1KFDHfvtV82LL4ZdiUj80506\nkXaaNw8WLoSf/nQjHTrUhV2OtMKBB1bx3nuwdm3YlYjEN20kJdIOVVXw2GMwahQMH17Nt99WUFxc\nHGibxcXFVFVVBdpGqjjwwGrq6vwW4iecEHY1IvFLYUGkHV59FdavhwsugMrKUubNm88dd9SSlZUd\nWJtlZaXMn/853bpVaNGndurbt45Ro+CFFxQWRCJRWBBpo7Vr4cUX4cADoXdv+O67SsrLO9C58wR6\n9OgXWLt1dV9QXr6ImhoNA4qGww6De+9FUyhFIlBYEGmjJ56Azp3h8MO3PJ6ZGew+FKWlwd7mSDWH\nHeaX5p43D2IwXV0kISlHi7TB4sUwZw4cfbQPDJK49toLttkGzYoQiUBhQaSV6ur8VMkBA2D8+LCr\nkfbq2BEOOkhhQSQShQWRVnr3XfjmGz8gTve4k8Nhh6EplCIR6FedSCuUlcFTT8Eee8CgQWFXI9Fy\n6KG+x+iVV8KuRCQ+KSyItMLzz0N1NUycGHYlEk39+vm1MnQrQqRpCgsiLbR6Nbz5JhxyCHTtGnY1\nEm2HHw4vveR7GERkSwoLIi305JN+1PxBB4VdiQTh8MNh1Sr44IOwKxGJPwoLIi2wZAnMneunSmZk\nhF2NBGHPPaF7d3jmmbArEYk/CgsiW+Gc3/+hf38YNy7saiQo6enwk58oLIg0RWFBZCuKiuCLL+Bn\nP9NUyWR31FEwfz58+WXYlYjEF/3qE4mgutov6zxqFAwbFnY1ErRDDvG3mZ59NuxKROKLwoJIBDNm\n+IV6jjkm7EokFrbZBiZM0K0IkcYUFkSasXGjX1dh772hb9+wq5FYOeooHxLXrw+7EpH4obAg0owX\nXoDaWjjyyLArkVg68kioqdECTSINKSyINGHTAkyHHgpduoRdjcRS//6w6666FSHSkMKCSBOeesrf\nv/7xj8OuRMJw1FG+Z6mqKuxKROKDwoJII99841fxO/JILcCUqn76U9iwwY9dEBGFBZEfePpp6NUL\nxo8PuxIJyy67wIAB8PjjYVciEh8UFkQa+OILvyjPkUdChw5hVyNhMYNjj/X7gdTWhl2NSPgCCQtm\n1tfMHjCzNWZWZmYfmVleEG2JRNPTT/tpkmPHhl2JhO3YY/3GUjNnhl2JSPiiHhbMrCvwLlAJHAIM\nB34NrIt2WyLRtHAhfPaZv1+tZZ1l3DgfHHUrQiSYnoVLgKXOuTOdc3Odc187515zzmm1dYlbzvle\nhR13hDFjwq5G4kFaGkyc6Jf7di7sakTCFURYOBL4wMweNbOVZlZkZmcG0I5I1Hz2md+G+sgj/f1q\nEfC3IjbNjhFJZUGEhUHAucBC4GDgduBmMzs5gLZE2s05eO4536vwox+FXY3Ek332gR49fO+CSCpL\nD+A104D3nXO/r//8IzP7ETAZeKC5J02dOpXc3NwtjhUUFFBQUBBAiSKbLVwIn38O552nXgXZUno6\nHH20H7dw5ZV6f0i4CgsLKSws3OJYSUlJTNoOIix8CyxodGwBEHHfvmnTppGXpwkTElvO+e2Id9jB\nb0Mt0tixx8Ldd/sptaNHh12NpLKm/oAuKioiPz8/8LaDuA3xLrBzo2M7A18H0JZIuyxa5HsVjjhC\nfzVK0w48ELp1g0ceCbsSkfAEERamAXuY2aVmNtjMJgFnArcE0JZIuzz3nO9V0F+M0pyMDPjZz+Dh\nhzUrQlJX1MOCc+4DYCJQAMwH/he4wDn3cLTbEmmPL7/0PQuHHaZeBYnsxBP96p5z5oRdiUg4ghiz\ngHPuBeCFIF5bJFpeegl69/b7AIhEst9+0KcPFBbC7ruHXY1I7GmdOklJ330HH30EBx+s1Rpl6zp0\ngOOP9+MWtFeEpCL9mpSU9Mor0KWLX9JXpCVOPBG+/Rb+/e+wKxGJPYUFSTnr1sF77/lR7h07hl2N\nJIo99vALdzWa5i6SEhQWJOW8/rof4b7vvmFXIonEzPcuPPYYVFeHXY1IbCksSEopK4N33vED1jp3\nDrsaSTQFBVBc7G9jiaQShQVJKTNmQE0NHHBA2JVIIho92j/uuy/sSkRiS2FBUkZVlb8FMX48NNqG\nRKRFzOC00/x25mvXhl2NSOwoLEjKmDULSkv9dEmRtpo0yU+ffFjLzEkKUViQlFBXB6++Cnl50KtX\n2NVIIuvdGw4/XLciJLUoLEhK+PjjDFavhkMOCbsSSQannQbvvw+ffhp2JSKxobAgSc85eOONLIYN\n8/PkRdrx5YfzAAAYSklEQVTrJz+B7t3VuyCpQ2FBkt5XX23P8uXpHHpo2JVIsujUyY9deOABP7tG\nJNkpLEjSmzVrDP361TBsWNiVSDI57TS//PPLL4ddiUjwFBYkqX30UQe++qofEyaUaRtqiaq8PNh1\nV7jzzrArEQmewoIktZtvzqJbtxJGj64KuxRJMmZw7rnw/POwdGnY1YgES2FBktbixfDssxmMG/ex\ntqGWQBQUQHY2TJ8ediUiwdKvUEla118PPXs6Ro9eFHYpkqRycuCUU+Cuu/wKoSLJSmFBktJ33/lp\nbWefXU56em3Y5UgSO/dcWLkSnnoq7EpEgqOwIEnpppv8NtT/8z8VYZciSW7kSNhnH7j99rArEQmO\nwoIknZISuO02mDwZcnNd2OVICjj3XHjrLViwIOxKRIKhsCBJ5847oaICLrww7EokVRxzjN8z4qab\nwq5EJBgKC5JUKivhr3+Fk0+Gvn3DrkZSRadO8Mtf+nEyq1aFXY1I9CksSFJ54AE/uPGii8KuRFLN\n5MmQluZvgYkkm8DDgpldYmZ1ZnZj0G1Jaqutheuug4kTYeedw65GUk337nDGGXDrrVBWFnY1ItEV\naFgws92As4GPgmxHBPzUtUWL4OKLw65EUtWFF8LatdqNUpJPYGHBzHKAB4EzgfVBtSMCfhvqa66B\n/feH3XcPuxpJVYMGwbHHwo03+p4ukWQRZM/CrcCzzrk3AmxDBPDT1ubMUa+ChO/Xv4bPP9ciTZJc\nAgkLZnYisAtwaRCvL9LYNdfAmDFwyCFhVyKpbtw4OOAA+OMfoa4u7GpEoiPqYcHM+gF/BU5yzlVH\n+/VFGps3D15+2fcqaBtqiQdXXAHz58Njj4VdiUh0pAfwmvnAtkCR2X9/dXcA9jWz84FOzrkfLKs3\ndepUcnNztzhWUFBAQUFBACVKMrn2Whg4EI47LuxKRLy99vK9XJdf7scwdOgQdkWSDAoLCyksLNzi\nWElJSUzaDiIsvAaManTsXmABcHVTQQFg2rRp5OXlBVCOJLMlS+DRR+HmmyE9iHezSBtdcYW/JfHI\nIzBpUtjVSDJo6g/ooqIi8vPzA2876rchnHMbnXOfNnwAG4Fi55xWTpeouuoq2HZbOP30sCsR2dLu\nu8MRR/jehZqasKsRaZ9YreCo3Xwk6r7+2s9nv+gi6Nw57GpEfuiKK2DxYrj//rArEWmfmIQF59wB\nzrlfxaItSR3XXgu5uXDOOWFXItK0XXeFE0+E//1f+P77sKsRaTvtDSEJacUKuPtu+NWvICcn7GpE\nmnfNNX7b9L/8JexKRNpOYUES0vXX+1sP558fdiUike2wg5/WO22aX6xJJBEpLEjCWbUK7rjDbwnc\npUvY1Yhs3UUXQZ8+fnVHkUSkyWaScG680c9bv+CCsCuRRFZVVUFxcXFM2srMzOS663I44QS/gJhW\nGpVEo7AgCWXtWr8F8Hnn+S2BRdqisrKUefPmc8cdtWRlZQfeXo8e6Zx11vFMmJDD5Ml+dUeNtZFE\norAgCeWmm/xufr/S3Bpph+rqSsrLO9C58wR69OgXaFtlZespLn6DysoK7rorh1Gj/BiGW28NtFmR\nqFJYkIRRUuLDwjnnQK9eYVcjySAzsys5OT0Db6e83H8cNMjPjvjFL/wy0AccEHjTIlGhAY6SMG69\n1f/SveiisCsRabspU2C//eCMM6C0NOxqRFpGYUESQmmpH9h4xhnQt2/Y1Yi0XVqaXyNk1Sq48MKw\nqxFpGYUFSQg33wwbNvh7vSKJbvBg+NvffGi4556wqxHZOoUFiXvr18N11/mxCjvuGHY1ItFx+um+\np2zKFPjww7CrEYlMYUHi3vXXQ2WlX19fJJnccguMGOEHO65fH3Y1Is1TWJC4tmoV/PWvfvR4nz5h\nVyMSXZmZ8Nhjfv2QE06A6uqwKxJpmsKCxLWrr/arNf72t2FXIhKMgQPh8cfhzTf9bYm6urArEvkh\nhQWJW8uWwW23+fX0e/QIuxqR4BxwADzwADz4IFxySdjViPyQFmWSmHLO8frrM/jmm1VbPffuu3cj\nI2M7evZ8gXvuqWlTe3V1VdTUqG9X4t8JJ8DKlX7Pk2231XoiEl8UFiSm6urqmD17EStX7kBWVtdm\nz1u1Kot33x3AQQd9xdKlbVtYoba2mvLyOZipX1cSwy9/CatX+9tumwb1moVdlYjCgoSkV68h9Oo1\npNmvP/MM9O4NEycOpEOHgW1qo7JyIwsXzmlriSKhuOIKP/Dxsstg40a48koFBgmfwoLEnU8+gQUL\n4Nxz/eBGkVRi5nsUsrNh6lQ/pfJvf4N0/baWEOntJ3Glrs6PDB8yBMaMCbsakfBceCFssw1MngxL\nlsAjj0C3bmFXJalKsyEkrsycCcuXw89+pq5XkTPOgFdegQ8+gD32gEWLwq5IUpXCgsSNsjJ48kkY\nN87PPRcRmDABZs/24Xm33fwiTiKxprAgcePZZ/0KdsccE3YlIvFl6FAfGA45BI47zq9oWlkZdlWS\nShQWJC4sXw5vvQU/+Ql0bX5GpUjKys314xZuuw2mT4fx4/1AYJFYiHpYMLNLzex9M9tgZivN7Ekz\n2yna7UjycM7/EuzZ069kJyJNM/OzhN57D8rLIS/Pb0blXNiVSbILomdhH+BvwDjgx0BH4BUz6xxA\nW5IE5s6FhQvh+OOhY8ewqxGJf7vu6n9uzjzT35I4/HD49tuwq5JkFvWw4Jw73Dn3gHNugXNuPnAa\nsAOQH+22JPGVlflehV12gVGjwq5GJHFkZfn1F158ET780P/8PPFE2FVJsorFOgtdAQesjUFbkmCe\nfBKqquDEE8OuRCQ4VVUVFBcXB/LaY8fCW28Zv/51Dsce24kTTijjqqvK2Wab4O9NZGZmkpOTE3g7\nEr5Aw4KZGfBX4N/OuU+DbEsSz+efw9tv+6CgxWYkWVVWljJv3nzuuKOWrKzswNoZPRpqawfy2GP7\n8NJL6Rx11Fv0778ysPYAevRI5+yzj1dgSAFB9yzcBowA9traiVOnTiU3N3eLYwUFBRQUFARUmoSp\npsZvxztwIOy3X9jViASnurqS8vIOdO48gR49+gXa1i67fMGqVX9m1apLePDBozjggHIOPrgskKWi\ny8rWU1z8BhUVFQoLMVJYWEhhYeEWx0pKSmLSdmBhwcxuAQ4H9nHObXXozbRp08jLywuqHIkzM2Z0\nZ+VKvwZ+mibwSgrIzOxKTk7PQNsoLS0mM3MNZ5yxhg8/zOHZZ7NYvDiLM86APn2i3155efRfU5rX\n1B/QRUVF5OcHPyQwkF/T9UHhp8AE59zSINqQxLVs2ba8/XY3Dj8c+gX7h5ZISkpL8zMkLrnEjwn6\n85/hzTc1xVLaLoh1Fm4DTgImARvNrHf9IzPabUniKS+Hxx/fnz59Kjn88LCrEUluO+7oe+/22gse\nftgv5qTeAGmLIHoWJgNdgLeAFQ0exwfQliSY3//eWLduG449dqW2nxaJgYwMKCiAc86BTz+FK6/0\nK6aKtEYQ6yykOec6NPG4P9ptSWKZMQNuusn48Y/n0KtXddjliKSUvDzfy5CRAVddBbNmhV2RJBIN\nLZOYWL0aJk2CffaBPff8T9jliKSkXr3g4ov97pX33gsPPOA3bxPZGoUFCVxdHZx6qh9o9cADdaSl\naZSVSFgyMvzP4ymn+J0sr7nGh3mRSBQWJHA33OCXpH3gAdh++7CrERHwgx4vvtgPeLzySviPOvwk\nAoUFCdTMmfC73/lfSoceGnY1ItJQ//7+53PwYL975XPP+Z5AkcYUFiQwy5fDscfCuHHwpz+FXY2I\nNCU7G6ZMgSOO8GHhttv8Bm8iDSksSCDKy+Hoo/2W048/rq2nReJZWpoPC+edB0uW+NsSy5aFXZXE\nE4UFiTrn4Kyz4JNP4KmnoHfvsCsSkZYYNcrflujUCa6+2g+AFAGFBQnA1VfDQw/BPff4ud0ikji2\n3daPMcrPh3/8w6/8WFMTdlUStqB3nZQUc889/i+T//s/OOGEsKsRkbbIyIDTTvO7wj76KCxd6nsL\ntZV86lLPgkTNs8/6XyjnnOPDgogkLjPYf3/49a+huNgPUp43L+yqJCwKCxIV//43HH88/PSncOut\n/heNiCS+wYPh97+HoUPhjjvgwQehsjLsqiTWdBtC2u2dd/x2uOPH+7EK2iBKJLnk5MDkyf6Pgkcf\n9RtSHXtsR3r2DLsyiRX1LEi7vPWWX2xp9939bYhMbUQukpTM/N4uf/gD9OwJ06fn8uyz+1FcrG7E\nVKCwIG326qu+R2HvvX1QyM4OuyIRCdq228LUqXD88d+zaNEAxo3rxo036tZEslNYkDa55x4fFCZM\ngKefhqyssCsSkVgxg3HjKpk8+RGOOaaSiy6CkSP9bUhNs0xOCgvSKs7BZZfB6af7x1NP6daDSKrK\nzq7g2ms3Mn8+DB8OP/857LQT3H67X8VVkocGOEqLbdgAZ54J//oXXHst/OY3mvUgksqqqiooLi6m\nVy/f2zh/fgf+9rcszj8/g0sucRx7bCUFBZXssktNu39XZGZmkpOTE53CpdUUFqRF5s3zUyNXrvR7\nPRxzTNgViUiYKitLmTdvPnfcUUtW1uYBS8OHQ58+2/DRRzvz2GM7cc89XenWrYShQ79myJCv6d//\nOzp0cK1ur0ePdM4++3gFhpAoLEhEdXV+3YTf/AZ+9CN48UUYMiTsqkQkbNXVlZSXd6Bz5wn06NFv\ni6/16OF/T0ycWMGiRbXMn5/Bp5+O5P33R5OR4dhhh2oGDqxhhx2q6d27lm7d6kiLcFO8rGw9xcVv\nUFFRobAQEoUFadann/oVGWfOhF/8Aq67zm8wIyKySWZmV3Jyml9wYexY/6irg2++gc8+M5YsyWDm\nzAxefdWfk5EBffpA376w3Xb+0auXn6K5acdajYEIl8KC/MCGDX5MwrXXwqBBMGMG7Ltv2FWJSCJL\nS4Mdd/QP8IOl162DFSvg22/9Y8UK+PBDqKjw55hB9+7QvXsXcnL2JjMzkzFj/GqSgwbpj5dYUliQ\n/6qshDvv9GvAf/+933nuf/9Xsx1EJPo2BwF/i3MT52D9eli9Glat8o8VKxzLl/fm6quzKSvb/Pwd\ndvDBYaed/PbaY8b4j7pTEX0KCymqsLCQgoICwP9g3nUX3HwzLF/ud5u7/HLo3z/UEpPO++8Xsvvu\nBWGXkVJ0zWOvvdfczO9u2a2bDwEApaXfU1z8BBdeeAzV1T1ZvBgWL4bPP/cfZ8zwf+jU1vrnDx7s\ng8OYMbDrrpCX529taPZW2wUWFszsPOA3QB/gI+AXzrk5QbUnrVNYWMigQQXcfz/cdx9UV0NBge9N\nGD487OqS05w5+ocr1nTNYy/Ia27mxzX07Qv77bfl1yoq/Dirjz7a/Jg2zd/qAOjde3NwyMvz/z1w\noAJESwUSFszsBOAG4GzgfWAq8LKZ7eScWxNEm7J1tbUwZw48/zy8/rpfonm77fwWtOee6wcYiYgk\noszMzUFgE+fg66/91O+iIv+45x648kr/9a5dfWhoGCJ22kmb4TUlqJ6FqcCdzrn7AcxsMvAT4HTg\n2oDalEYqK/0PyezZ8O678NprPmV37eqnNj3zjN+vXj8YIpKMzGDAAP+YOHHz8e++2zJAPPkk3Hij\n/1pW1ubbFyNG+DERQ4f68RGp/Lsy6mHBzDoC+cCVm44555yZvQaMj3Z7qWzTaOLlyzc/li6FBQt8\nd9yiRf72QqdOkJ/vpz8eeijstptfVOnAA8P+DkREYq9PHzjsMP/YZN06PxNjU4B4802YPn3zXhcd\nO/oZGEOH+hkd2223earnpo89ehBxvYhEFkTPQk+gA7Cy0fGVwM5NnJ8JsGDBggBKSQzz58Nnn/k3\nZXW1/7jpUV0NGzdufpSV+Y/ff+9HC1dVbflaPXr4FD1iBBxxhB9lPHTo5rnKAB9/DCUlJRQVFcX0\n+wSora1lxYqllJfPYvXqJYG2VVNTyZo1y4A6amvfJTMz2CHS69Ytp7R0NV99NYv163/4vZWWruGz\nz14PvJ1oSvS2mrvmif59xXNb0XqfN1RRUUpl5VI++ugjunXrFtXXbig312+ON2GC/7ymxvdCLF0K\ny5b5j0uX+t/Xa9b4weGN5eT4xzbbbP6YleV/B2dk+EfHjps/3/QxPd0HjU1jKI44wh/fmgb/dgY6\nb82ca/2ymxFf0Gw7YDkw3jk3u8Hxa4B9nXPjG50/CXgoqkWIiIiklpOcc/8M6sWD6FlYA9QCvRsd\n7w1818T5LwMnAV8BFQHUIyIikqwygQH4f0sDE/WeBQAzew+Y7Zy7oP5zA5YCNzvnrot6gyIiIhKY\noGZD3Ajca2Zz2Tx1Mgu4N6D2REREJCCBhAXn3KNm1hO4An/74UPgEOfc6iDaExERkeAEchtCRERE\nkkeSzggVERGRaFFYEBERkYgCDwtm1s3MHjKzEjNbZ2Z3mVl2C553hZmtMLMyM3vVzIY0+vpbZlbX\n4FFrZrcF953ENzM7z8y+NLNyM3vPzHbbyvn7m9lcM6sws0VmdmoT5xxnZgvqX/MjMzusqddKVdG+\n5mZ2aoP38qb3dVmw30Viac01N7M+9b97FtZf0xubOU/v8wiifc31Pt+6Vl7ziWb2ipmtqv93dqaZ\nHdzEee16n8eiZ+GfwHDgQPz+EPsCd0Z6gpldDJyP34hqd2AjfiOqhutZOWA6fgBlH2A74LfRLj4R\nNNi46/+AXfG7fL5cP8i0qfMHAM8BrwNjgJuAu8zsoAbn7In/f/d3YBfgaeApMxsR2DeSQIK45vVK\n8O/nTY8dAyg/IbX2mgOdgFXAn/CDrJt6Tb3PIwjimtfT+7wZbbjm+wKvAIcBecCbwLNmNqbBa7b/\nfe6cC+wBDAPqgF0bHDsEqAH6RHjeCmBqg8+7AOXA8Q2OvQncGGT9ifIA3gNuavC5AcuA3zZz/jXA\nx42OFQIvNPj8YeCZRufMAm4L+/uNh0dA1/xUYG3Y31u8Plp7zRs9t8nfF3qfh3LN9T4P6Jo3eM5/\ngMsafN7u93nQPQvjgXXOuXkNjr2G7xUY19QTzGwgPmn+d3Fx59wGYDY/3IjqJDNbbWbzzexKM+sc\n1eoTgG3euKvh9XL469zcxl171H+9oZcbnT++BeekpACvOUCOmX1lZkvNTH/h1mvjNW8Jvc+bEeA1\nB73PmxSNa25mBmwDrG1wuN3v86DDQh98l9R/Oedq8d9EnwjPcTS9EVXD5zwE/BzYH7/D5cnAA+2u\nOPFE2rgr0jVu6vwuZtZpK+c095qpJKhrvhC/jftR+CXQ04CZZtY3GkUnuLZc85bQ+7x5QV1zvc+b\nF41rfhGQDTza4Fi73+dtWpTJzK4CLo5wisOPUwiMc+6uBp9+YmbfAq+b2UDn3JdBti0SBOfce/gu\nSADMbBawADgHf/9SJOHpfR4c8xsz/h44yjm3Jpqv3dYVHK8H7tnKOV/gN47q1fCgmXUAutP0plLU\nHzf8wMWGSag3MK/JZ3jv1z9vCJBKYaG1G3dRf7yp8zc45yq3ck5zr5lKgrrmW3DO1ZjZPPx7OtW1\n5Zq3hN7nzQvqmm9B7/MttPmam9mJ+EH/P3POvdnoy+1+n7fpNoRzrtg5t2grjxr8AIquZrZrg6cf\niP9HfXYzr/1l/Tdw4KZjZtYFP8ZhZoSydsX3aHzblu8pUTnnqoG5bHm9rP7z5q7XrIbn1zu4/nik\ncw5qdE5KCvCab8HM0oBRpNh7uiltvOYtofd5MwK85lvQ+3yztl5zMysA7gZOdM691MQp7X+fx2Bk\n5wvAB8BuwF74+1UPNDrnM+CnDT7/LVAMHIl/Ez0FLAYy6r8+CLgMP01kR/y9r8+BN8IcxRrWAzge\nKANOwc9AubP++m1b//WrgPsanD8A+B4/Qn9nYApQBfy4wTnjgUrgV/XnXI7fQnxE2N9vPDwCuua/\nr/8BHogPv4X4acPDwv5+4+HR2mtef2wMfqrYHPyYpjHA8AZf1/s89tdc7/MoXnNgUv3vksn43oJN\njy4Nzmn3+zwW33hX4EH8vNp1+HmeWY3OqQVOaXTscvwUyjL8qM0hDb7WD3gLWF3/9YX1FzAn7P/R\nIb7BpgBf4aeYzgLGNvjaPTQKUvi5uXPrz18MnNzEax6LD3LlwMf4zcBC/17j5RHta47frfXL+q+v\nAJ4FRof9fcbTow3XvK7+90vDxxeNztH7PIbXXO/z6F5z/BTVxte7FvhHo9ds1/tcG0mJiIhIRNob\nQkRERCJSWBAREZGIFBZEREQkIoUFERERiUhhQURERCJSWBAREZGIFBZEREQkIoUFERERiUhhQURE\nRCJSWBAREZGIFBZEREQkov8HRMH8h27TgBsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0eff509b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = app1_ru.sample_multiple(100)\n",
    "sns.distplot(sample)\n",
    "np.mean(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ожидаемо, модель руководсвуется данными, полученными на американском рынке. Давайте теперь покажем рекламу 2000 раз в `app1` в России:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UDmue+1hb2yREIoOIx6N5I5KmUnF4vV6kUmpE0X/842nnsddff7aq5zWSQGFH\nBBmdncDate6PFdY4RKOV99fTowoyiYDsZ5rdnIkaS9MEG7m9RdLpCO6++8fO7wceqAbd2muvg51l\nTzyxFVOnqpOXXbfR1pYNNrScKVv9/mDJv9vaOhGtrZNwzz1X4eST2/KCnmQynhlRVEM6nca7777k\nPJa73mhasUL921G6u6vvqrh6tfq/lqBopAFU7vamqbIttRZ6VmpGicWA3l73x8jd0FBx8FmqGWWk\nBgZGN1jp7R397rmp1Ph25SYaa00TbBxwwCzn5/7+pUWP779/fldVIQSmTlUntL4+taytbSfn8QkT\nplT1d4UQmDx5hvN7KNTn/GwPY+7xeBCLpbBo0as45pgTAaDqOo5csRiwtPip5Ukm3S+epU7Y6XR2\n4KTNm7OvxUdBLKa6HVfTjbgWq1aN3+Bp9WQkvXPWr88Gn7axCDYMQxUkb95ced1qdXSUzuYN1/vv\nq38fdUuXqiJyanxNE2z8+79fht/97lUAwLJl1+Q9ZllpaJrXKRy1eb2q26V9gfV4PE4zyMSJlYMN\ne93cQCYUyv6NbLDhxbp1KxCPR3HBBT/DhAk7IRSqMHqVi+3bqy+Mq/au6P331cBJgGqy2LixtmOy\nrOYJUOLxbJNaOfZ70MwFvbVKJFRGrb+/8rq1GovmwGreZ9rxTFN1j6fG1zTBhqZpOOKI2a6PWVYa\nQnix776HFT02dWr+xdIwZGZ/OoDiMTxyPfTQOgD5WRUA+OY3r8L3v/9HpFJxp9vrgw9eD1334OCD\nP4HW1on4wx9+hI6OdXnbud3Jlfo5d1lvb/FjsVj+74UXRilVVmOkJ/LOThWgjEfKNxYb27+zcmV1\nd6jV3mlt3Fi6e3OzSWd6l8fj5derRblgzrJUkejgIOs33PT38yJN9aVpgo1yksleAF7svvv+ecuF\nUMFGbhtuKqWqEU8+Wc3smlvH8cADq/HFL14AQGVSpkxRzScHHHAUcrW0TEAw2ArTNJ35UUKhPhx9\n9EnQdY/TE+XJJ+8Y8XMbHFRpXLfsQm4xXW5QsWULsG7d6MxdUmk8EDfr1uWnsaWsLgW/apWqCRlL\no3mx7OsD2tsrr0fuyjWj9Per7sDt7cPrmVIPPbTG0oYNpYPidJr1IDT+mjrYmDXrBABAZ+ffAHhd\n15k6VV2M7SJRr7cVAHDYYScXrbvnngdi9uyvAAA+97mvOsvtsTZsHo8PPp8qKrWbUhKJKGbM2BPJ\nZDZ/WzhgcyvMAAAgAElEQVT42HBUU51vGPkFi1u3jl5B23CaEkIh1WRjSybHr6h1NC8y9dKMsmSJ\nGvhrLPT3q0nu7NctXWFuwdF8TaqdjLDSMVFWLKZuMqqpB+nvz/+ejqa+vuLsKzW3pg42/uM/bnZ+\n7u/vLHo8HgemTFEnSPti/PnPz8fMmZ9DIHAofvjDO3Dppb/J2+ZTn/oi7rvvAxx++P9xlgWDbXnr\nJJNxpwdLbrDR0tKGdFrg1ltfxowZu6Ozc33F55BIqOI5KWu7UBae9D8KX+xmv1stxbJGv8jVZu9X\nSnXhWb7cvW6o2teed9Q71qpV1a+7YYN7IW0sNvKC2I0bazsWanxNF2wceuinnZ9zm016etw/2R6P\nym7YEfzee5+Gk09+Gd3dOk499SJMmjS1aJu99z4k7/fCEUxnzTreCTZSKRVsxONRBAJt0HUvDjjg\nkzjxxLOqGthr61bVLbBUM8NoVewPFSRZEgl1Qql2v412oa81eKtHhe/ZWMh9jezxToY7emdfn7qj\n3pFzyuzo9zydbvxMTGenyow2Wq3M4OBH46arXjVdsGHPk7LzzofD6/VVWFuZPj1bC2CfjIY7QuGt\nty7EgQfOQiDQAgC46irV3JJIRBEMtsLr9cI0NQQCbYjFxm7u7FrT2esLkix2U0ulC0O9NCXUyjBU\n7YibagORap/7WFxcQiH1no11T6DcpoyRBrbDncDO/nvlepBs3Zrtwl2N8QjU3CxfPrxaqd7escte\nVbKjXqvRkkqp1669feTZlMJmRape0wUbqZQ6k5166otFj0kJnH76k7jggufylk+fru7a4nEVrU+b\npn4fTl3DIYccAwDYeefdAQBr1rwHKSWSyRgCAVUPouse+P2tiESyc5RXc7fo9gEvdwEYyRfCHtNs\nPAfcKlTtRanc3zWM2otKFy8uHvOhknJ3eW49UqRUxzXc18z+vIykC2c8XvlObyTvaTqtgiKbJzNt\n0HCPedmy0uOXbNlS3YR+jXqR6OgYfl3Ohg0jq4kqvBGxz4u1fkd2lPb20atpsoP7Rsvq1IOmCzYu\nuOAazJx5EKSclndi+eIX30I8Duy775dwwAEn5W0zfbr63z7577abuoh3Fpd5VG3atN2cn9PpFEzT\ndIINj8cLv38iksk4Egl1ti81WNdwT44jyTiYZnb71aurb5+t5qJeS1fQWk+Qbq9VZ6f6Z9cKVPt6\nlroI5wZA9mvU0aGKNGvR16eOy+31MM3xuSiuXFn5Ts8+qVbKbLj14lm5Mj97VGsAKyVgWRZSqRSs\nzIH09SURj8eRTqedbuX2MWrjfDaLx6u7SQiH84MuwP27smZNbXfe1WZy+vtHr+kqN0sXj4/sczpe\nWdGxmLRvvILWRYvGrkh3vDVdsHH00SfihhtWARB5X8bp0z+FoSH1ISk8KbW2Am1t6k21LMDnA2bM\nqC3YuOuupfif/3nd+V3XdefnSERdUeymFSA7Ff3LLz/uLBtOmtrexm0MiuEW4yUS2f1aVvkMT+4x\nV3PyqyXVnWvAZQy0wnEEPvyw+C7MVu2dSOEJcHBQfeHtSeTcxi5wO7ZKyvUiWrp0eCOQLl06OkV3\n0WhxT5CuruxdndssrIXflVgsm8GwAyp7u8KsoWGYSCaTMAzDCSBsqVQKoVAKAwNRxGJxpFIGIhEL\n4XAKoVAM8XgcyaQKPKr5/tR6kUilSjdVFQZTpaxdW7ye/XpJmW0eiUSqryno7VWD8Y0kiMjddvNm\n9Tm3g6BS39PC1284TYTVzJo83PPEWBtpgBSLVT/wnT3Ts/1/o3dZbrpgAwBaMtf0wi+ufXfh9oGZ\nPl2dNO1gZI891Jtc7Zdpv/0Ox7/8y2fyltlNKn196tNiZzYA4F//9d8BwDlRVsNtNfv4Bgbyu7MZ\nxvBnSzUM97vE4RS3WdbIMkQ2t8nYCscRSCSK25ft51Ep2Cj1vOxxMuJx9fpWajcfrfbtchmgoSH3\nJgPTHHkBXCqlsln23ZT9mct93oWfw8ILg2VZWLw47mQk2tuBaDSGSCSKdDqN3l6Zly0zDAORiIFw\nOIlQKIpEIgHDMGCaJtJpE1Lq0LQgkkkNqZRAIBCAz9cCwId4XGBwMIlQKIZEQv3N996zqhp4rZoL\nWnt7dlTd7duLP0e587lEo+qCXct3pLdXpfhrHfzNziTZd+3btqnve+5dvGmakFLCsiwkEgkkk0mY\nOSvkZg7t99v+rlabDahmPcNQz7EwgC114Q6HVSBVmA2qJ5XOA6XG61m1SjVrVcM+l9hBe7VdluvV\nRybYmDBBfXgtK/shz/2wT5+uPkCGAei6CjZMM9vODAALFtT2Zl900S8AuAcbra0TM/v8C9IFZ6da\n0n6l2iI//HD0U5x2cZthFJ90SxVVrlkzOgNxDfeOoppgY9u27JDt5ZS6q7BPBtGoe2ZlJHdDbq9d\n7p2224VtOJPLAep52N8Ze7/V1AIVPr9kMolYzMoEEPFMRsJEJCIRDqcQDseQSCScphDTtCCEDq83\nCMPwYWjIxOBgHOFwDOk0YFl+RKMe+Hx+BAIt0DQdmiYyzZEBeDytAHxIJFTgEQ7H0dkZz2t+cVMu\nCySlhJTSec+7u9V3rVzhuB0wuAUxhTcUdhbHPrxyg7+53QkXXrC7ulRA/t57aSQSCaRSKUSjCQwO\nRhCLxRGNmhgaSiMcTiAUijpNUWaJk021n9ly55h0Wn23tm5V51Y7MLOfc6m/Yb/mO7LXUiVdXSqw\ndPs89PSo72A9ZyH6+4d/MzpcnsqrNJ5gUH2QYzFg770/D8sKY9IkOM0obnbdNf8LPGkSMHGiikI/\n9jG1fGBAvUmHHlrdl7G1Vc1E29vbmTmu7HgcdnfZt9/+O0KhMKZMmQw79htuT5jRVO75LVumxifZ\nZ5/K+4lE1JlFG2GD+lgGG8DotOuOdttwKlU5UHN7PB5Xd6hTpqi5f6r7Wym8/bYJr9cDj8cDXRcI\nhyOIxTQAXng8Hucza39P3GtLJJJJA1Lq8PuDsCwTiYSBZBJoaWmBzydgmgZiMQPr1ycxbVoC0Sig\naX4IocHn88Hj8WHFCgsTJ6ahaQKxmFa2+NOyVOCRTnszzZMGQiETg4Mp6HoSPp8Gn089Lyn1nO1K\n7zMSSSAcNhCJeKDrHnR06NA0rWgbFTSZ8Hp1bN+uQ0oPgPwPq2VZiMXiCIUkkklvZjsDAwMWYjEN\nqZQXmqbBk7mzUcGClmmK1cveCRuGAcvSAGhIpVJIpdIYGLAQjapjTacDSKct6LoGj8cLj8eCYZiI\nx00AaQwMmNB1IB73QNfVc4zHLQwOppBIZJdFo0mYpgUpdaTTHmiaOj4pVfBrGKrp2TRVs9Fee6kL\nciikbt7yPiGZz0ypU8JYzfY7GgrPQ1u3qmtHLjurYRiqSb4eqXqo8f2bTRlsCKGyG7EYcOaZz2Pq\nVPXB3rLFvWYDUIFFa6uKvu0vxx57qAzBPvuofUqpHt+yRRWRVmJnL7q61O3u5MnTXdfr7e1Da2sL\ngPyp7NPpFKTMflrH88tXKTYobJIqdWypVBLJpIWWFh+8Xu+4FIXZoxPusUf2eaxbp7Jbe+1Vflv7\nfd7RDKM4i7ZpU+Xjtw0Oqn+zZlVeFwBisRSiUQFdT8HjSSGREPD5JEIhCSHUMp9Pz1ywPdi+PZtV\nswusk8kkBgZUSsTv90MIAV1XF+vW1gBiMfX6qoueFz09ErFYGn19Jny+7BUplQJMU8PgoB9e94F/\n894n+w7SsoCuLuHsPxhUF+NEwkAsloaup2CaAsmkF7quZy7m2Q+kaZpOUPzBBxaGhlQGBUhB0wCv\nV8PEiRoMQ21rGKqZJ5EA0mmJeDwFTUshEkFOcCMRjSaRTgPJpAfRqAUhrEygFkA8biIcNqDrEpqW\nhK4LRKMmwmENup7G0JAsuuin0ybicS+SSYH+/hTCYSAS0WFZKhMTDLbA69UASKxerTkXvBUrACG0\nzGPqhfV6LRiGgXjcAmBA0yS6uiTWrxeZ82AamiYRj1tIpwUMQ2WnNA3weARiMaC9XQVL06drCIXU\nslWrsufR3CBcZXOE8x7mfwaBQKDiR9XV4KD6zkybNrztK+nsrC5DOzSUzQpWe64bHFRBy8EH5y8f\n6XnIslS2a+LE4sd2xDluWLebQojLhBAbhBBxIcRCIcTRFdb/NyHEIiFEQgixVghxXsHj5wkhLCGE\nmfnfEkKMqPU5GMxWS9uZCnsgGrdmFCGAXXZRP/tV7Sb22ENtY7fPVZPyzGVnNjZvVvmqUsHGuece\nhETCwrp12Zx4JDKEY4/1Y/78WwGo1NxIJ/WSUuLhh29Gb2/l1EmtQUG5sSlSKSASSWXajYf3Ka/l\neDZuzLZB524XDo/uoD7VZjIikdJtvJFI9eliex+1vBZr16pMlK2vr7iuZMsWA4sXC3i9Xvh8LbAs\nH6JRibVrBfz+YN6ySCSJgYEI1q7Ntv+HwwmEw1Gk0wY2bxZYudLnTGSYq7j5RSAa9SEQCDrrb9mS\nbd4Yzgmx8LX0eDwIBAJoaWmDx9OCVMqbKTBNIhxWBaapVArpdBqhUAxdXRF0dkYQiaiAye9X9SGa\n5kcqpSEcVk08g4MRJJNJJJNAMBiE3x+E16vqSBIJHYODaQwMxNDdHUcyCei6D4FAILNeEIFAEJs2\neREMBhAItMDjCcKyfEgmNRiGBr+/BboegGH4EIsBoVAK4XACiYSJREJDJCIRjRpYvVrDmjVBGIYH\nhqEjEAhC13UIISBE5dO7EBpM0we/PwC/Xx3HwIA/85wCznFoWgBtbW3YsKEFfn9r5ti8iEQEwmHV\nPDM4GEEkEs0U+6YRjWabbOysSygUQX9/2FlmGAbefddyxsDYtGl4mY1aurfG47XV1kSjlQMNKbNj\n39Rat7V5szovqaA1u3yk56rOTnWTNRa9cYaj5mBDCHEWgBsBXAXgSADLADwvhHCNKYUQewN4BsBL\nAA4H8DsAdwohTixYdQjAzJx/Vd7DuQsG86vqd9pJBQv23ZWbXXdVd8L23fDMmaqXip3CtSwVeW/a\nVN0H1c5sdHauw8SJU5wBx2zf/e5vAdjtuR4kEmmnjXnBgr8AAFauVH0qc+c2Kcc0VWW/my1bNuKm\nm+bh2msvrLif3MxGYRq0kF2EVsiyLFgWMml5P6JRCxs2xGGMYHAIKaUzuV3ldYvf62rGYrCVanO1\nLAtSSmzYkN8+X5juVsdqoK8veyIsDBi3bx/beWHC4WxNSSQCrF9vYM2a/LNPe3sKhqEyDkKooKO1\ntRWpVCuE0JxlgUAQHk8Q6bQXkYiJcDiBaDSO3l51d59MavD7/U5Pq0LVXDxyCy7LKZUCLjyxxuOq\nW7LqRaTD7/cjEFAXfMvyIRxGps4jgVQKWLMmgFWrPAB0JwCyMzQ+nz+TNWhFe7sfyaQOj8fnXNSF\nyNaRtLS0wetthZTq9cj97qvXVMsrelYZB3vbVgghoGk6fD4VCAQC6gIP+NHS0gK/Pwi/vxWBQAt0\n3QOvV61XTYCRS8r8mye1vTdvP5qmw+v15r1/9rJAIOgEKVIGkEzqiEZVb6FEwkQyiUxwZKK9PYmB\nAZXhiccFIhEDAwPxTI2NquMJhVKwLDNTM1PTUynJrYcZUHwxL9W0UE1wv3lzdT2Tyvngg2zt2Gj0\nxinX3b9RMhvzANwmpbxfSrkawLcBxABcUGL97wD4UEp5hZRyjZTyjwD+ktlPLiml7JVS9mT+VXl5\ndWc3o9gXnNy263LBhq7DSd0KARxwgLpTtj+I++6rTt7VXLR8PpUT3LhxJXbaqTirMWfO93H66d/G\nzjvvBq/Xh1RKOIGCPUlbIBAs2q4c0zQRjxtIuHxa335bDXRWqfdLrV1vk8kkBgejeYWuUkrEYvFM\n8Z/IDGQWRCqlUsGpKqqnVAo6hoGBPieYUT0XUohGSwctdnCUm8Wq5fnYShUDx2IJLF/+LhKJRCb9\njMyx5a9nGAai0SQikRjS6TS2b5dobweGhqRzB1iugLEU0zQRjcYqFkDa69rFmIYhEY8nczIR6czM\nxBJSannD7qvvTfGLJ4SGri5/5iIXQCqlIZkUzkVc191bZgcHs7VIzzxzJy6+2L19p5rSnt7eLqeA\n8777rsXAgEpj9fVtRTic323Jbu7bujW/Fsq+uAeDQQQCbVixIohQKOhcQO3vrjsNsZi6uHtLtfNA\n1Sn5fL6Sr4k6jopPN2d/KvgQQjgXErf3qBYfflh8DG5fq7Vr3e/us3VuqvbE6w04WR5NU8GZz+eH\n3x9ELNaKjRtb4PMFM0FVC/z+Ngjhh2F4EItJhMNpDA7GEA7HEInEnCxJbiGrypKknN42bqQEkkmr\n4nq5VqzIjpejioNTmV5R+dvan71cbsMDDOetsZ9m4eFWOvxGGAa/pmBDCOEFMAsqSwFARQgAFgA4\ntsRmn8o8nut5l/XbhBAbhRAdQoinhBCHYAQmT85mNoRQGYnWVvt5FK8vhMqGzJkD7L57dvlBB6mg\npbtbXbza2lTzyqpVlT8AuSeCyZN3dl1nr70OQm9vF8455yB4vT4kEhbS6TRSKRUshEK1t52oXgXF\nGY7nn58PAHjrreexfPlbNe+3nPXrNYRCSSSTSefLaBgqQrfbwYUQ8PsDkNKHSCSNWCzuerG0Tw7q\nC2/htNP2woUXznUq+A1DpcsjETXAU+E+7AtW7uBk5eSeyCqtb1kWNm5cjQsvPAYPPPA7DA2VDhpM\n08icBHSEwykMDKgAIZk0kUxKhMOqt4ZqXjKqCvLsE2Du9vF4vGS2x7IsRKMmBgcTGBqKZO7cvEgk\ndITDaUQiiUzGLj8bUc2xqIuf37m7Lic363PDDRdj7drFiMWK+zMXvow33/xdrFjxJq68cg56e7sQ\nCvXjzDN3x333XYPu7g7cffeV+P3vv4fu7g58+cu74gc/OKXkMeQWtKbTKTzyyE2Ix5OZ76kHW7dW\nV8I2klFbR8o+/nIZoEqZsng8ikhkCAMDPejuDhcFeG5p92g0O95Drtz3a+3abHd0+wYj9xxoZ2vs\nHltCqOLebGYmCMtqRWdnK6T0IZHQEI1amXFWYhgYCCMSiSIaTWJwMImBgVhR000iYUJKlUl8990k\nurqSCIUSCIdjiEbjTk8dFUQY2LYtig8+UMtisew4L9FoFAMDSSxalEBXVxSRSCynl08MoVAssyyO\ncDiJVCqddw5Q3bZVkLR6tWrSSCZTTuBk/x11jstfZlm1F29WGga/s3PHDXdvq7VAdBoAHUBhjNsN\n4MAS28wssf5EIYRfSpkEsAYqM7IcwCQAPwTwphDiECll2QKDUheHiRPVBcnjya5jByCF20ycmI1M\nJ0zIv7vaZRcVpGzYoD4AmqYKeV54QQUgM2eWO7qswUH3RM3kyTMAAJs3r4Wm6RDCi3g85cwWu3Fj\ncYHIc889jFtv/Tk6O7OPhcODCIcHMW3arpnKdi9iMRVs+DNFKBs2rHTWf/vtF3HYYaXiw1qHKZew\nLE+mgC0N00zA51MfrUAgUNR+r1KyOuLxJAwjjmDQ59whSimxfHkcu+4qYRh+DAz0IJGI4oUXHsUV\nV9ydyToJvPnmM1i69FUceuivM10k/c4+qu2BotaxEI0moGkCgYC36E7VMAxomgZN05xszcCA+tbe\ndtuP8a//ehR23vkz8HgM+P0qtayKBw0kk1bm7tYPKX0wzVSmO6gJKQUCgRanZ8brryex224p7LOP\nB1J6Xe9YTdNEJJJELCYgpYZAoAWGkc5kslLwetNOYaId4KkMkgafL4hw2IBhmPD7vQgEVAGoaRoA\nZFH6vZpxKipZseJNvPbaE/jOd25wns+LLz7kPN7b24m99joob5vcpoVweBBPPvlHPPnkHwHAuSDZ\n+3n66dsAAC+//AhefvkRAMDSpa/l7a/URfn++6/D/fdfi4kTp+Dyy79Z8jksXPg3/O///gnXX/90\n5pirm8agp0e9hgeWOCs+99z9mD59d+y223Fl91P4Prg1DRaqdId74YWHo6tLnTv23PNAPP54/rjj\nhd+b3t4uTJkyM2+gwlQqiaef/hNOO+1bznsC1BaIqWDDbbkGj0eD3+916uc8HhOWZSEUMrF2rYbD\nDgtA0yxYloV43EQ0qgpc33gDmDlTYnBQQyol0d7uQzDohZQm0mmJZFJ1AY5EgFDIQkeHhmRSYvLk\nFMJhAU0DBgetTIG2Oi/FYlZmJFsLUqonqOteGAaQSll47z0Tuq5uLFThrAbLsjAwYGHJEg2miUyB\nsYVQSHP+hsejAbAQiWgwDPV66LrAwoWqmU3TVHD24ouPYvfdjwfgfsNaaO3a/EJZKbNZqcmTVea3\nms/RaKuL3ihSyoUAFtq/CyHeArAKwCVQtSEl3XLLPAQCk/KWHX/8XBxzzFwA+cHF5Mkqwit8kffd\nt/Rw4UKo3ij2NO+apppbJk1S2Y1KwcZZZ/0AjzxyI3p6XOZqRjbYsKnsholoVJ11ly17A9u2bcbM\nmXs469xww39gaKg/04yg3sLzzvskOjrW4Y03VEZE1z2Zi2MKQggkkzH09/dgl132wtatmzBz5p4w\nDMPpbldO7t8ppIZitwBoMAwvfD47iFB53lJpXiE0BAJBpNMpLF78DmbMmI5wuA8/+MGXcM89S9DT\nMwkeTxoffqgaMX0+PzTNj3g8CV3XcfXVaoK773//fLS0/AvC4RT8fgN+vxfBoDpWdScrkUym4PV6\nXbvfWpbqGZBOC6TTKQBpqK6eKuiIx5OwLMDvVz0xDAOIRLJXsLvuuhlXX31ipiDOgK4n4PdrEEKd\neO1ATwiBQMCfucCnIYR02vg9Hi8sy8S2bWlMnpxENGrA69WLjlkNygQI4YfPp5bb20tpZQIcA7qe\nht+vwev1ZJqSBDRNg9fry6v2t/9+Ndrb34fX68Oee5a6pyh2991XYtGil7Bo0QLMm3cLDj3007jv\nvmucx3t6NhcFG08++UcceeTnsPfeh2Dr1vwimAULHnZ+7uws3UDe2bkeu+++HwYH84v1cjMb69ap\nfPnAQHfZwusf/UhlSmKxCFpaVNf1Su3pyaR7sJabaLz+elUjf9RRxVF9bqBfeGyJRHYcoWp0dbUj\nGg3hgAOOzFtm6+hY4xxXR8caPPLIjbj88ludwCIWC+PMM3fHJZf8GmeffQUA1Vz15S+r/p6RyCC+\n+U33U7RlWXjppT9jy5Z2nHfez4se7+mJ4Mkn78Fxx12aF8jYcpttUikdwaCOwUEvNE0FfFOm6BgY\n0OHzZYMSy1KBRyJhwbIkfD4fTFNkLuxKIAB4PKpX0IQJAoAOj0cFA5alugYD2VGedV2rWLfm88nM\nucRCMmllRqIOwLIAKS2k0xZSKXU+sCwVOCWT6m8ZhrpBsJs07aBG0yTWrl2Mn/1sLp5/fjZ++cvn\nMjcyAoZhIJ024fFoCIdVUbEQGqTUEA6rHkHBoJn5zGt47rk/4/nn50PX1Q11Mgls3z6+M+zVWrOx\nHYAJYEbB8hkAXAZyBjLL3dYPZbIaRaQKH5cA2K/SAV155W9x/fVP5/074YS5mDCheN0pU9T/tUZ0\n++2XPcFomtr+oINUqq5SQdull/4GAHDIIZ90fXzKlOxLoy526gMZjyecC83y5W/mbWNP4NafM9pP\nR0fxydfj8ULTfIjF0vjc51TRyvXXqzvAZDKBeDyJRKJ4qLvck93ixa/h6KO9WF8wWpX9GqbTKSST\nyAQ02SDCMPTMXU75F9vr9eGyyz6LM888AL///Y/R39+N7u4OBAIBCOHDhg2qa0Jb207QdQ+CwVb4\nfH4cdJDqAPXqqxtgGH74fEEkkwKRSBKpVBymaSIWA9JpA/G4am4obO7o6FiXGVhK1cb09GzBBx+s\nRDicQiymBj2yLMA0dcRiqgujes7Zq80uu+zhvNaqV4Uf8TiQSFhYtOhlrF+/HL/61QV45ZXH0NGh\nXqdt23zo6clvttA0HcFgAH5/W6bK30QolG0iMU0TqZTMnDi9RdkiVYPgywx65Uc8LhAK2YWfnhEP\nZX/BBYfhnHNUYNDZuQ733HN12UJfy7KcuqP165fhsss+k7k7TOCUUy4CgKIA/JprzsbNN38XP/jB\niYjFwliw4KGi/RaaMCF/IJFAoAX//OeTAIoLdnNHpOzp6cgs6y/5WoTD2XHor7jiC67rxONRtLe/\n7wzcB6hiQVvud8ke8n7Zsn86y+6//7qifebWgxVmGAuDmLfffg4LFqjm0c7OdWhvz+bSY7Ewzj57\nP1x88VGYPVtgyxb3QrOlS98AADz44C/xzDN34Nln78Ls2QJDQ31Ys2YRAGDDhmzbzE03Xer8fM89\nV5esh3jhhQdw3XVfx913X4mzz96/6PHf/OZbuO6672HFCvX3e3o25zUH5mY97PNs7oB2hqFe69wC\nV03T4fF44fX6MwWzpW92VAZQfY/Unb6WqS3zOzcJ1bKbiFSPLlW/1NWlO8ejioT9eceoAo8WeL2+\nzPF4nULfQKAFXm8L3njjGQDAkiVLnJqWgYE4IpE0wmErU+CcdnorvfdeNNNcFEckEkc4nEB/fwSf\n/ewZ+OUvH8EvfvEYHn/8cdxzz5O4/PKbanqOI1VTsCGlTANYBOB4e5lQ7+bxAN4ssdlbuetnfD6z\n3JVQOd1/AeDSSpjPDiAKtbTkj/4JFA9wVG3QMXlyNi1l32iecYbqIlvNzIf3378Kv/71U66P5RaO\nvv/+65nj0pBOp5yZY3/606/lbaNS38Dy5Sqd/9RTdzmPvfzy47Cs7JffsiyccEJ2MLG2tknw+4NI\nJmMwDKCraxv+/Oc/FNUc2OePN9/8OwCgPfONVnfwMafOQdc1CKEX3SH7/QEEg60VC9js5iIAWLLk\nHwCArVs7AKiLqn0Ha1+4pJRYvPhlJBLq7DM42It0Wr1my5e/huuuOz9Tz5DA0JAKOlS/fh8iEROR\niAo6hob68eUvH4D77vuV00Z96aWfxoUXHg1NU6NRRiIpWBYyvQSCAHyQ0oN4PBthDg3lR5u67sH6\n9RTWXvkAACAASURBVMtwwglt+OlPT8dFFx2Jv//9Hlx99VcRDpevv1GpVLvnRzZoUMFPAlICa9a0\nlt2HfQx2l01d90PXPfjgg/wLl9uIqYahRvS8997/wuzZAmeeuQdisUjRxeS2236Me+/9L2zatLJo\nH5HIEDZtWo277vo51qx5L++xnp7N6O7uwGc/ewamTJmBTZtW4pVXHsNf/vI7PPDAL/HSS+qiOTDQ\njfvvvw6PPHJj0f6PPPJz2G+/I5zfH3tsM0499WIAwB//+Ab22utgbN5ceubA9euBnp5O56K8YMHD\n2LbNvTF7+fLsXEfvv/86enryx90Phwdx8sltuOCCw3DeeR+HYaRLfo9y5QZRd91VfMefGxQVbl94\nTvvJT07DtdeejTvu+Bm+/vUDcMEFhyMWC+PFFx/CRRcdlbfun/6kMhMzZ+6NI46YjZNP/iYA4Ec/\n+iIA4NVXHwMA3HjjJQCAt956Bk888QcAwMKFzzr7yR2cEAC2bVNdrTZuXIm33no2c9wSN9/8XWed\nrq71zqSTAPCtbx3tvN/vv/8GBgd7MWfOnrjtth8XvR6AXYiePwx4qSCx0nndvnFsb3fvZrtkiXtT\nlKqvUDcc/f3dWLBgftnC08Ib0dyal2rmhxFCOMFeOByCaZrw+1VRrcfTgra2NgSDQQSDbZnvegDh\nsB/ptI5EQmTGgwkAUF2j43GBaNRCT08C/f1x104EY2k4vVFuAnCxEOJcIcRBAP4EoAXAvQAghLhe\nCHFfzvp/AvAxIcSvhRAHCiEuBXBmZj/IbPNzIcSJQoh9hBBHAngIwJ4A7hzWs4IKCtra7P2r/ydN\nUl9W+wu7zz7ZIKLSB3T//bP7BVQq7sADVbBR6S5xr70OQluby8gqACZOzEZL8+ZlY7J0Oolp03Z3\n28TR1aUaj+1eJgCwePE/0dW13smSXH75CXnb6Lq6A08m1QftiSf+iN/85ntYvPifrkWO9kU+mvnm\nmKaFeFwiGk1kekPITK3J8BoAX3jhwaJlV131VWd//f0qYZZKJZBMxvHWW89i3rzjsXGjutDdfPNl\nOdvNwauvPoaenjiE8CEclojHDViWzGQe1HgRnZ3b8MgjtwAA7rzzGrzzjgqohobURedLX5qR6WkQ\nhBDZMSPsO5RYLIxgsBWnnfYtrFlTXI1n31kX+vDDMhVcKB6R0w4avN4gTNMLwFPT6yyEQCQyhNde\ne6Liuul0Cscf78Nxx3lwzz1XA1A1Fe+99yIefPB6Zz3DSDtNEPbrZevp6cQpp+yEc889GM8/r04B\nJ5xwNmbNUp9ru+lrt932Q39/Nx555EZcffVX8Yc/fB933vmznNfBdHqY5Jo8eTquvHI+7rprCX74\nwzswbdquCAZbMW/eLXjiiS049NBPY/r0PdHb695kCai75e9//3PO7729nfjZz84tWu/FFx/CT396\nOqZMmYHzz/8vAEBHR/bOIhaL4MILD3d+D4cH8IUvTMB///dFefvJ7Q7Z17ctM5poGIcd9q9FfzMS\nGcKqVe/mFSwXXstyM7Z2kSOgshK2f/7zKVx33TecwQSz+x/EqlXvYNu2jZgzZx5+8pN7MHnydESj\noUxaPz/Lef3133Q+O6FQP66//nwsXPh3vPjig2hrm+Q0n3zta/vAMNI477yP48c/PhWAyrjE4xF8\n/evZ4GHBgoexcaPKVNqB6E477Yw77vgpzjhD3XQtW5Zfc2N77bUX8P772QFj0unS41BU+orkNk3Z\nwUvhPCyFkyt2dKzBHXf8DCeeGMDQUB/+8If/i2uvPbtktshNJKLe46efvj3T9Fz5WN9//w189rNf\nyhyD+vyFwwJS5p9z7cyKnR1RWVI1fk1u12i/P4j29gno7vaNe6FzzcGGlPJRAP8J4Bqopo7DAJyU\n01V1JoA9ctbfCOAUACcAWArV5fVCKWVuD5XJAG4HsBLAswDaAByb6Vo7bIXBhqYBp56qmkUA9cXd\nY4/i7dyC1Y99TI2UOGlSdp+HHabuRu3shscD1+ab3GMopGka/vrXPqd98Le/vQwdHWsQDg9g8uSd\n8ZnPnI5PfvJE1wjavlPITfcmkwlceOHh+NWvzgeQzZbYLMsPny+AZDKWKRxS6eQnnrgTN998RdFc\nCUNDKm/ZkzPPsRoIyItQKAnLklVniNyUqmWxT3xDQ73OYGhXXTUHL7/856J17WO2C9W2bduYCQxa\nAPjh9WZHYfV6vTjrrL1x++3ZO8qrrpoDAGhpUW+e/Xra3SNt3d0dSKdTmWBjAqZO3QWDg8UXRbsn\nke2WW96Crnvw4YeVJ9Zxm6/DbiIpNX5FOb///ffw859/Bf395Ucleued5wGgKOBcvPhlzJ//a+f3\n7u4Op5bi7ruvdJYbRhpz5mS/TL29Kt+/776H4bTT1J3yqlXvAACmTt0FBx5Y3PV15szs0DrPPXev\n8/Ozzw7ihRfieOKJrU6z46mnXoTHH1d/w+PxYOpUNSLfjBl7Op/pUuzxb664Qt3L5DYR2B5+WD3n\nI474N3zjGz+Frnvy6kQuueQTRX8nlUri73+/p+g13LDhA8yeLfDlL++CP/3pCixY8DCmTdsVl112\nEwKBFkgpcdJJrTjllJ3w7W9/Escd53Her2xXSJnJKP0PHntMBceLFhV28lP6+rZg113VHAsnnvh1\nZ3l7+3I89NCvMGPGnvjUp1Q245vfvBoAcNJJlQtBnnvuXicLcs01j+NLX8o2p5x//mHOz1u3bnTW\nu/DC6/DnP6sL8g03XIzzzjsEnZ3rIITAf/7n7Tj44Pzm5d12y285j8ejOOecg3DeeSfhwgvnOMu3\nbMlvrspV6ny0bt1SvPLKY3juufudmy27XqVwNufC5qpzzjkIDz2kgu533nnO+Q489tjNefupZP78\n/8aNN16Cv/zlz0XH+re/3YPZswVmzxb44IOFSCRiSKUSOOaYk+HxePHBB6oxoL1ddcsvNRsxkN/J\nwZ5IMNdIu0wPx7BGEJVS3iKl3FtKGZRSHiulfC/nsfOllMcVrP+alHJWZv39pZQPFDx+uZRyn8zj\nu0opT5NSlr8NrEJhsAGoJpFyNZFu74HHo8a4P+WUbFOMEKqXyv77q5S0YahApNRY+OXe24kTpzh3\nT089dQuuv/6bGBzsxcSJU9HWthOi0Qji8QTUpFXZYMBO52/atAbnnnsFPvaxQ/C3v90LQN1FvPzy\no0V/q61tClpaJmFwUNV7SKlOjC+88CAefvhGPPvsw4hGs7cMdo+X7u6ezPoy83x80HVVJ1FYeLll\ny4fYtGk1Vq58Gx98sNBJPbqxv0DZ49sJALBo0UuQUmLr1g34+MdVr5m33no2rzeDzb4weDzqxf/W\ntz6RqXPIFlBWogpJ45g+fQ8n6MiVSiXx1a/uhdtv/wni8TBaWiagrW0nRCLqNmn79i248cZvo6en\nE6FQtpbmhhuew8c//instdfBTrAhpcTzzz/gZJ9y5aZvS40PUKmnUO42dmZo7drFriedzZvXIplM\nOJ8D2zPPqIDrySf/B9FoCL/5jQpGVq506rid9PfgYK9rweasWSfga1/7odMcaNtnn4n4xjd+CgA4\n99z/h8svV6Pkfu1rP8QXv5gdrufKK+fjxhtfzDT9BTK9rMo/9+nT98SmTasKAvC4c/GWUiIej+CM\nM76DU065EMcc84WiZoGurnaEQn3Yc8998cMf3gmPx4NddtknL1PQ0VF6FqvcQlYAePHFbPbObhqK\nxyOYOXNvJBIx3HHHz/KaGADg9df/N+/3np7NePjhX+Oaa/4DF16oLuT/+MfjmDlz76K/f9ttP8b2\n7Vtw3HFn4Wc/ewCXXXYT/n975x1fRZX+/8+5c/u96Y0kJCSQAKH3qoBgQVEQAUVBbKtgX+tX/bmK\nZd1V17WtvaGiuO4qgl1srAoqxRaVIh1CTQiE5PaZ3x/PPVNuTUICAc779bovyJ25M2fmzJzznKde\ncsk9qK3dja++mo8BA05S34myMtLO8Hd0ypQ/4+qrH0V5ed+o4+rJyWmP9PQcVWul1/pMnUpFkwYO\nPBmSJCE/vxTnn69prqZN6wxFUZCVlY/Bg42+MKtWfY/KyqV44IFLUVm5FD///JV6rwsKoq9VD3d8\njTfW3nDDiZg9+2z87W8X4PbbJyY8lh692RQAlix5VxWc58//V6OPAwA7d5LJadasaVi06CP1+2Aw\ngPvv1579K64Yqi7E8vI6oEuXAeo5Obt3x88qzZimrYlXgfZQc1RWfeVwLUNjhLjIYjp6OncGiotj\nb+vZk6Ta1auTn8ftjr9t6tSb1P//9tu3WLVqGZzOFDidKfB4DsDrVeDz+QwPvtfbAK+3ATt2bEZJ\nSVcUFRmdsO666xwAQIcOFejSZQAAcqArLOyEzZvXh3PnGz2S7757Bh5++H54vZQvgzue7tzJV1r6\nnBRmOJ0umEwSvvvuI8yZQ5EG557bCTNmVODyy4fgiiuG4vrrI112iJtuOtWwOvvwwzq8+y6J67fe\negZqanZi795dGDv2Qhx/fPTgwJ1Ely4lJyq9BmPSpEIsXaqmg0Fd3V488shV6oomEoqqCaJ9+3I0\nNNSpK3MOj6LYuPFXNDSQsJGSkgGvtwGBgB8ffPAiFi58BvPmPYC6OhI27rhjHgYNOgUA0LFjT1XY\n+OWXb3DffTNw4ok2rFz5BaZP7xLlZ6AoCkaPNuNf/4rMfac5ztXV1UZdU3X1dowaZcK3336IU09N\nxcqVnwMA1q5daTj2pk2rUF29HdOnd8HJJzvwxhsPqtvd7jSkpKSrf9vtTvTseRwA4N57pwMg9TcA\nTJiQiwkTcnHBBd0BaJMXAAwdOg4mkwllZb1x0knT1e8tFobjj5+IuXNX45JL7lH9b9zuDFx//VOY\nOvVGAMCAASdhwACjGTBZ0i+u4Tj9dKN5cuLEdvjb3y7Cp5++ji1b1qhmjOHDx2PTpt+xY8cmbN36\nB8aOdeO888qwZ08V/vSna9UIlMLCMlWgamjQYl/118WZM2e2wSTBTR167HaX2ga+Ytbz0EMzsXy5\n9m58991Hhu1r1/6I999/HoMHn4prrnkM8+atw7vvVuPyy6kf/X4vamp2gjGGs8++ThXYAaBjR00L\nkZ/fUf1/aWkPzJx5PyZPvgZXXvlPFBV1BgBcfvmD+POfn1D369ZtCAoKOoIxhltumRPVds4DD3yo\n/v/44yca2gAAXbr0x8SJV2LxYgUPPvgRTj/9UlRVrceVVw7D++8/jyuvHKYKapIkxczLwnn33edw\n3nlleOKJG7Bnjyax33HHFNxzD2l39P32/fcfqe9GMvTOv1arXQ2z5uj7mjsMRyLLMu6993zDYmnJ\nkiXqu7xpEwlr9947Hz16DANAwqQkSSgr640OHSqwevUyw0LC44lfrv5QF1lrDEetsMGYVoAmUrIr\nKCABQk88R1OAHEGzsqKPD5BAU1ZGCVX8/virTsZov3iFhmKFZZ5zzg0oKuqCTZt+C6vvQ1iyRBt0\nfL56bNu2AYqioLCwI9asiR2/e9FFd+Guu97Ec8+tDF9rPvbt24Px47NjqmI3b96CmpoAtm/fgvp6\nEo+3bKEVsiwDTz55Az766BXo66HcfPOpeOmlO/Hqq3+NOt4vv3yD/ftrUFdXi61baXW4Z08Vvv+e\nrmXkyMn461/fgdPpNtyH6mpKsZKWlo2hQ6OTNY0dS+GDfDDXv4i1tbsxa9aJaGigieyttx7H/PlP\n4N13n4l5j+rrSejiK8ULL+yOyy4bgI8/JiVcZeWS8L1rhwMH9sHpTFW1MPv3V+P990klv2nT79i/\nvxqnnXYxxozRHHs7duyJysol8HobVGEEAK67bjS2bFmD6dO7GFbjXDB5991no7QbfMWycOHTmD//\nCSxf/gmCwSAmTSpUQxJfeeUedXBljOGHH75Qf//00zdjxowK3HWX1r5ffvkG+fmlmDt3Nd54g/xh\n/v3vjQBIqLXbjWr2f/zjk5j3Uf99cTFFr9jtTtx++6tRVY/5ZDZmzLno02ckhgw5DRaLFZdf/iAW\nLfIiLS0LimL0idq6lUxNkRWcS0vpPU1L017Uiy7qFVZJk/bso4/mqMJSTg5VUhw+fDwA4JxzSjBt\nWrlBmB80aAg6daL/t29frgobPPojLS0bV131MD74YB8WL1bwyCN0j7dtW4cXX9TCQWtrybelQweq\ntNWuXQmuv/4ppKdnIy2NnMZGj6aFwdCh43DccRMAADfccJKqVp8zZ7bhPn/zDeX9OPvs6zBp0tUo\nKOiI1NRMTJ16o6ptOOGE8yHLFCa6d69mtsrP1wa/rCwtdv/aax9XBfa+fUdh7tzVWLxYwdSpN2Li\nxCvwt7+9ixtueAZPPbVU1Yzo6z198kmDqql48cWfDO9yly798eSTS3DrrS/jxBPPw9SpN6mCId3r\nUzBs2OmIZNGi19C160CcddY1qjZWz/z5T+CFF+7AP/5xGQDgzTf/iccf/zMAYPXqFVi8+L/49NPX\nMXIkg8ViNENed90YNYdLIvbsoYXHq6+uUk2kBQUdMWdOJRhjmDlzID7++FWsW/eL6jD8zDO3IBgM\norZ2N+64YzJOOEFSBadp024FAPz88wY1q+1TT5GA3b//GFxwAZknn3/+/6Fv39HIysrHwIGnYPPm\n1VGa4HjE8/184IE/Ydmy2O9ua3PUChuSpPlXRBbGsVi0bKLNRa/F6NOH1N/xcnXof+NIkH18ypQ/\nG/7OzS1C+/bl4TDOA5AkK+bM+btqt66v36eq7N3udLhcNPnZ7U7ceqvmo2u12pGfX6rG2tvtTlRV\n/aG+OFOm/BlnnXW1uv+yZd+ittahhrtWVAzA9u3bwsm7gAULnlLzBETy/PO3x/z+jDOycPrpGZg2\nrRy//PINJk3SyuYOGXKaOsACwKxZD8Bmc2DWLLLnpqZmYsyYc9Xtp59+Kf7xj48xceKVmDbtFtVR\nsb5+H/70J2Mo4a+/koDFr5UPRCNHTjJkvbzvPnIS7NePLICyLGP16hWqZ/7WraR5IPPUG2jXrkQN\nu3z55XuwY8cmOJ0pWLHiU/z223dRGTX5xHrnnVPi+hRcffUIAGQuuvhi0hD4fB6MGWONUrMDmr/N\nPfechzFjLNizR8t/xwels866GlOmXIctW9ZAURT8/vsyvPEGhWNHOuNVVAxCUVFn5OWRwJKXR+o8\nhyP6ZSkr621w/uOkpGRi5sy/Y/ToczBggLH80Qsv/Kj6WejJyirAAw98adCmcP+UykrgtdeABQuA\nZcuAr78Gvv0WePtt4M03gf/9Tys2ZbeTNuTEE88DgIQ+MikpmeFz50dte/jhz3H77XPRr98A9T1v\n374cmzevwpo1K9VnYv78HUhPz1Z9QPr2HYXXXluLnj2H4403HsSZZ+ZBURRUV1dhxIizcOqp5Ed1\n3HETVMfwP/3pr8jOLsAdd8zD4sUK/v739zB8+ISoNlVXb0efPiNVP4mXXroTpaXd0b69UZu5ZQtw\n0kmPo3fvM7BnzzTMnQt8+CGwdWs6Ro16DW53CSorh+Ltt+neVVYCWVnka8M1LX4/+UToF2nbtwP5\n+adj5MjLDEIeF05MJhNsNgduueUl/N//vYhOnXqFvzdex9ixM/CXv7yGyy9/IOoahw49HffdtzDq\n+379RofNWBsjnGcp4uWVV+4x7M+dWt977znD9w0NdejdewTefrsKF198N1yuVDzyyFWYNKkQH3zw\nUtR5AXr/nnzyBgDGZ+X5539AaWl3DBx4MjZs+BX33TcDF1+saYxef/1+vPTSnbj44t5YvPgtwzEH\nDz4VkyZdgKqqdaivJz87LgA4nSmoqBis7ssFR56P5sorh0e1kWs39uypwosv3mkYK77+egHuu+8C\n1NXVwufz4P33X8CNN54S81pbm6NW2Cgo0MwoB+Jr31oEt5uyiv74Y3z7GB+0iospiVj37tH7zJr1\nIG6+mcJYubMjXw16PAdgNluwe3cVxo+/FCUlXVFVtUE1g7jdabjttlfCv3UiN1dz1ous82C3uwzm\nk0mTrsXZZ2vq+p07N4ExE5YsWQjGGPr1OwErVnyH9eujQx0bgz6XCABcddVxCbenpWXD5/OoA4vL\nlQa73YkZM0iQmTr1RgwceDIACh3evXsr/ve/+di3rxoFBZ3w2WcB3H8/heB98gmFHOtVqABw8snn\nq5oJQHOQ7NnzOIwfP0vdPxik2go1NTuQlpal5gHIzS2C203Cxh9/kJT53HMr1ONt2mT09OzTZxQA\n6tf//vfRmPdpw4ZKKIqihihyQqGgGn3D+eKL/2DBAvJ1iLQp67n22sdQUTEIu3Ztwb///RCWL6fI\npchETMOGnYHp08muzicIxhgeeOBDPP200Vb82WcBMMZw2WV/w6JFXlx99SN47LH/4Y03NsBsNuO8\n8/4Pd975hiFR04EDQGZmJ2RnG+2VkkQ+T6+/DsyfD3z3HU2YPNpg+XLSUGZmUv6JhgZg+HDgpJPI\nabu2lgSQp54C5s0Dli5lOPnkuxHJjBl/wezZmg/TqFGd1WssLe2ham7Gj5+Ffv1OwEknTYMkaSuK\nwYNPhcVixcyZZLqbNOmacIIlo+alffsy1SF2795deOutx/Drr0thNucjPZ00G3V1B/D553Rtffpc\nhldf3WZw2MvOjl03pkOHbqqvCwD07j1SzWiqKBSy+emnwM6dFejbdyEsFhv69QPy8oD+/YHZs8/D\na69twOjRacjPJw3ZypXA0KHzccopX2DhQglffQV8/jnw8cfAG2+QQPfpp8BnnwFffklC3ty5wPvv\nA0uXkvn40kufxBNPLANA7/Jpp10Us/0AwkmuYm8zmUwYPvwM9O8/Bu3aleC99/Zi1KgpmDz5WhQX\nd4Hf78POnZvUENSbbhpr+P1f/0rvOvej2rFjU5TAO2LEWcjKyscFF/wF8+aR4+qePVW4//6LcdFF\nvdDQcABLlrynOn6efLJTDT91uTRtZkUFCZjcvBiLuXPvU00w3boNwZAhp6F//zHo1m0wcnKKVJ+M\n774jc9Mdd5DGLCUlXTV7T5hwOQDqe87IkQznnVduCMXeunUtZs0ajJdfvhu33TYemzatwjffvIv/\n9//OxMcfv4IFC57CE0/coO7fmFoxLU2byCDaGkgSDZq9esX3t4iHvh8a67TbsyepeJctA3r0iN6u\nj4hJTY1tUzObzRg37mJ06NBVzb9ht9OqcteuLUhLy8b+/XuQmpqLnJwiVFVtNAgbDkceKioGYcqU\n61Q1MRAtbPAkOgBw2WV/Q35+iUGF7/U2YO/eXfjiizfRr98YnHbaTLz22oP46aelGD7cKBiQKSX+\ngzt8+Pikqj+n0xgW7HZrGWGHDDlNvZbp029Dv35jVC0BQBlYg8EA/vKXswAAvXuPgNlsxqBBNBC9\n+OI/ccEFD6lJnDhWqx2hUHQwfV5esUH4ycxsh9raXZBlGdnZhWp0zpgxU1VH0k2bfkPv3iPQvn05\nHn30S1x77SiDpz5A2plu3QbD7U5HTc12pKRk4Nlnl+Pcczth3LhL8P77JGTW1e2NEiwA4I03HsTs\n2ZqtmIeRAqT+fvTRq6N+w4WE/v3J7+Gpp27C8cdPRP/+J6J3b9KijBw5Geeee5MhKkD/zA8erA3o\nM2b8BStWfGTIOmu12jB58rWG8+7eTRNWTg5QWEifd98l1W52Nr0rNhtNgmVltG9qKkV7bdpEya9M\nJm2x0K8fmUl4imX+L69h5PWSFvP77ymPxv79nTBjhh87dryKTz65BNOmPYKpU6+Gy2XCCScoyMyk\nKtCbw4/EnDmkAamsXKr6nCxZAnzzDbUpFALy8jqhT59RWLbsE1RUDMI115DA+OmntOpPT6d9c3OB\nwYOnIy/vL9i5c5OqSautLcSaNSRsyPIoVFXRfeLF/lwuul+ZmUBlpTaAdOp0Gtat+wAAUFY2HL/8\nor3Xxx33T7xH7kqw2zXV+ckn0/0MBqldetLT6cND+RUFqK3tjz17oH5qamhBVFREEQ/V1dRfY8bQ\n/jU19Nmxg0fiXY7vviPBIzOTTM6ZmZQBdPt20iRnZtJn2TLycUtPJ2f79HT6PiODroEx4KGHFkFR\nFJhMJtx1FwmIXMjfvHkVFix4StXOAcC4cX/C5Zc/gJSUDNx++2u4995peOihy/H99x/h3HNvxuzZ\n/8ZZZ+XD7/epWi+ATG69eh2Pn3+mJGvr1/+CU0/VnMP1mubHHiMt4Cuv/GbIl3P22deruVIkScJF\nF92FYDCA999/3uD3NWXKdRg9WntnXa4iVFdXIRgM4pdfvkZWVr5qSgOAhx76BHv37kL//qnYtAnw\neMz497834pJL+uDAgVps2/YHpk0rw6JFXmzd+gduvvk07N5NwseKFZ9hxowKQ79/+eV/1JB1gMxN\n/fpFh1+3JketsMHpH2OREGtuPNhIILsdGDiQVlkFBdE+IJHpbhOdjzsIAVAd1G688WT1u6ysfGRk\ntMO2bWuxb19NuPy1HR4Pw9NPfwcABqdBbl81mUjI0a/yJ0+mFyolJQM33PA0XK403H33uZg4sR0k\nyYwRI85C+/adYLXaUFu7D3v3Rsdb8ZVELMrK+qj2ZX5tlZVL0LPncbj99rnYuPE39OxpVA06HNoL\nP3nyn+FyUYIcm82Bvn1HGfbV24wBqCtnvb149+5thjYAJMRdeOFsvPLKPaopqmfP4WCMGdSQ6em5\n6uqkuLirmgwqLS0bNpszfP37VM1Fnz4jsXhxbOErNTULixf/Fx5PPa6++q8oKOiITz/1wWKxYuzY\nC3H11cfjjDM0n4OXX/4NHs8BzJo1CF988aYqbOg1GWlpWTjrrKtQXb1dzbUwc+bf8cwzt6Br1wHq\nPqmpmdi/vwbV1dtRXNwVHTv2BEB+QZHhh/G45JK7ce21dyfUFCoK8MUXpIHweGjS5nTtSlqA336j\nichsBgYNokmrqAgYNox+v38/qfG3baNJs5SCG1Q/rMicCHY7aRbtdqB3b140zIJt2y4EY25IJ12F\ntAAAIABJREFU0ll4800T0tKovECXLrGdtYuLh8JioXavXk3m0ZoareiixXI6gE/g81mxfTtpVbZv\nB0pKaDLetYvqUgAMEyasx5tvlqG2lnTceXndMG1aJwwcuAXBYHukpWlt3b2bPnv2kO+XJJnw+OPb\nsX37Luza5cG6dR+gX7/7UF09DdXVQO/el6KhoRq//WaD1Qocdxy1c/9+GoMSpTPnQt7WrVpV5IwM\n+uhzCfEihvze0zVQv+md6YNByknBBZCaGq1+DGO08Nq7l8I1eaGwUaPo/Hv3kraKW0bsdi6EMGRm\nMlUYsVgo+sVud2L58kWq1gEg34mbbnpW1QzxsWThwqcBAPn5PeB2Z+Cll37BmjUrVcdmzmOPLYbf\n78XJJ0fftJEj6ZizZj2impiysvJhteajupqb7pz48MM6fPTRHEyYcLmqzbvootl44okbUF29HTfe\n+ExUhFtubnvIsozZs8/GqlXL0Lv3SIN2KyUlA127ZsDhoPvi8VBo+Pvv78VDD83CwoXPwO/34fzz\nKwyRQGlpWeqCiDNr1gOqtrSwsAzbtv2BZ5+9FVdccT8OJUetsHEwwkNRERCRnVvFZqOVWix69iSV\n8NKlwGmnaW2w2YAOHWL/JhmRYXkAOZqtWrUMP/64GDU11XC706Lipm02TZvBY+75LiNHTsaaNSuj\n9hs/fqbBkzoUCqovZ0pKGrzeBoP5hQtt+hTJAPDFFyF1stfbQh96aJGakXD06HPQrl0HQ24FDvev\nkCRzlHARiV7YuOuu/xi2TZx4JebPfwL33HOe4XunMwVduw5Er17HYfLkazFv3oOQJAlnnkkJwrgK\n86STpqOy8hvVF2LmzPuxZctqFBaWISMj16DRiVcfQk/37kPx7be0SuWOgdzm3auXUR17++1zUVJS\nYfB0//zzNzF69NmGBE7/+hdpqS699K+46KLZ8Pu9cDpTcN55/2c43vXXP43Zs8/G6tXL0KfPSKSn\n5xiEot27aSIpKiKNgqKQ2lyS6HkvKEjsbwTQZLl9O02g2dkUKu7zkeBAkyRNHIWFNPFUVZG5xOsl\njQBAz2haGn0qKqLPES8aRf/4u1ykMSkrM2HkyLNRX0/XtmMH/bt5M5lrDhwg4SMvj4779dd0vdyf\n65RT6F6sWkXXVlZ2NpYsuQYNDQwf6YJDhg/XQt4DARI6du82obT0JPzww7No164vrrpqDNxuIC+v\nPdq1o+v77Tc6l8tFAgtAAoDPBzgc7dCrFzlvnnZaFRyOdqiuJgFn+vRnYbFoSeDM5vjjS1aWMR8D\nY/RdVpZWTp3Tty/dE4tFS62up6CA2rp9u2YuNptJI5Ojm8O7daNz1tRQu/hY6vWSlrmwUF/KnYSk\n2lrav7aWngt9vhm3G8jIMCE/v7cqaPTp8xf06nUWOnfug8pKTWOTl9cBU6Zch//852GkpBSiunoa\nXn0VSEsrR1paOX78kbTd+/bR/fvhBwa324FHH63HtdfGduRbvboI8+ZRn6Wm0vWkpdEx3G4gPd2N\nwsKrsHat9uz+8QfQs+dDSE2lZ85iIa2Ow0HbTSbyy+AJAEtL/4xly2iR6nTSPvHmMO5oDBhDjp94\n4hs4nal4+OEr4PM1qOafPn1Gqvs888wynH46mX//+9+mhe0eLEetsHEwxEvM1asXPQB8wHM4jMlc\nJAk44QRyaPvjD22lkJvbNM2GnszMdhg+fLxhZV5U1Bnduw/FvHkP4I8/KuF0poaLBxlP8t57eyHL\nIYOHPgBMm3YLnnvuNsRCb6IAtMnc4UhDQ8N+QxhYba2MQMCElSs/h9lswcUX342amh0GrQIXdACg\nW7fBePhhMi907hytcuKalwEDTsT48bMwc+bfYTZbEt4rfSG7UaMmG7adddbVmD//CTVpU//+J+KM\nMy7DiBFnqSsQxphaYIpzwglTMGTIaVi48GksWjQXt956BgBaXb3wguYFrBfwYkUT6ZEkCm/mKtfS\n0hi2Nh3cfKY3gd111zmor9+HefPIue7CC+80FEZLlFOEmwdCoZAh9JGzejU5Wi5bRpWOU1MpGZDL\npdWeyM6myaKggP7PL3/7dlrJ6gX0UaPoX5uNVsd8hWyxGCe8vn3Jf4kxmpg2bUp4W6KehaKi+Jkk\nOS4X+Xd0DD+KfOX/5Zc0EaxfrwnOJ56oCUyFhTT5WSx0T/Lz83DzzS+gd++RcLlIqMjMNObW4cJU\nYSFw330Poa7uduTmFhnazQUrpzO67SZTtFDHHROdTmMSQkmi8yWr8qqnMeH5icIm+STIn4nSUmP4\nZWEh9XlBQXQ6gfR07buyMs3Mw9ukF36CQZrMa2pIANq9GygqmooNG8gkO3HiXZAkhtpaek55NkwS\nvP6JO+74JzZvJq0AFy727aO+3bzZKIClpwP799NDkZMzBN2734gvv9TGkpNO6gq3m35fW6uZlHbu\n1I7Lo6QiteZcK8txOul3+/dnYcKESixY0CN83zti40a6zvp6uubsbLqfwSA9F2lpNDeNHXsViopO\nweuv34vS0v6QJB9yc3PQpcswWCzA44+TyWfz5mp4PPtRWlqEAQNOwsyZf0dKSnrS4qCtxVErbLRG\ngrRIgaFDh+ikKgMHkrf88uVkU062GkwGYwz33bcAL7zwF7Vok9lsUb29//jjB7hcaTEHHL13f+Qx\n42G12jBw4Mmqd3RaGi1Z3O501NXVGpI6XXrpNNx55zw1B0Ws6AS9VO10pqgrdd5+PWYzwpURHbjh\nBnJ+LC5O7ODLNQT6MtccLihxM8mNNz5jEH7iwRiD0+lWTQ1a+2K/LiNHTo75vZ527YBt22x4/vkf\nsG7dzzGvf+HCPVi58nNs3bpWjc5hjGHkyEmqRzsP8QMap03hFBR0Uv8fmb1z+3YaLHk+Ga9X82c4\n9VQa4NaupX0qK8mp0G6niaOwEFixQps0x42jbWlp0ZNWURGp67kZhIem88dRl6wVDoe2eu7alQZx\nn48G3b17abKqqzOW0m4sDodRSOHaCJMJGDyYhCA+aUROHuPGaYmX9LWWysuNqckBMoFyMygn1quX\nktK4svWxSCZsRJ5P/3d2NmlsIkmWyyTy/HoSjXd6TVW8BR1A78qOHZpA2q4d9c+YMVeiqmoiZNmG\nDh20C1EUmqD37tUEgtpamujHjYuOPCwupn2XLaPnND+fjjF06HowlosdO/bhyy+BG298Dh079kD3\n7t0QSSzBmIcZ79tHY1Z5ObV/9266p/v2ac8rtbk7hg79Cd9//xomTswGY6QdX7eOhH+HgwSNtWs1\nAZiQAHRFnz5zYbXSmNnQQI67djvdW6sV2LYtC0AWliwBBg/+BOvWUVsGD45dd6i1OWqFjUNBrJfS\nZCKBY9s2MqeccELLCD4XX3w3XnnlXjUKIze3GGlpWaiqWo8+fUZBkmxJV9d63n67Ku622257BRMn\nkgqXT9guVxrq6/chFArAYrEiEPDj88/fUD3PE5Uev/nm59UVus9HI3xk3gaAXsSqiGalpsYXNqxW\nIBCQ8MADH0b5bgBapdhQKIhp025JKmjYbEZNVd++Wg0NHiUUyaJF3qgw10j0Mkp5eR+Ul/eJuV9a\nWhZOOGFK1PcjRkyKCp8bOvT0JqUc1keGtG+vzdCKQuaD1FQyc7jdNBhnZpKpwWbTctKUl9P+WVnk\nl7Fpk1ahtG9f+v7442n1VlMTPRjzgTYjg96JSOdFPV27aitdPoFxjUTfcHLLRBNWMvS3jmsjuNOi\nfnuyVyo9nSY2xug+rYlfAw5A7Mk4L08TNhpzjIICmlTWr4+e7JtCfn5sYUNP9+6xi/ZxWmNRl58f\nnT5clukZLopRX4Ixem7d7ujyE8XFdI/0lWFdLnpW9QIe9R+p38rLXXjrrW2q/1dxMfXb6vhJYwHQ\ns6IvacG/s9k035PINg8d2gtDh2oLD7OZ3r2iIhJoMjPJLFVTQ4JHXR199u+ndqWm0pi1f7/2Pd8n\nJYVMfPrf1NQAdXV2dOt2PXbt+h/27DEWS2xNjlpho7kvQeTvmpKPgyfscjiAoUNpQF6/XlPfHgyM\nMSxcuEe18ZvNZpSX98Py5YvUSbUpxMovwNE7UfXqlYFNm2ji3r17K9av/wWDB5+KbdvWYcOGSjVm\n+8Ybn4t3OIwbd4n6/1tvfRnvvvtszIkyVlXnRIO93U5SvT5iQg9jDOnpOaiu3o7CwrImrwJtNitu\nvvkFZGbmxUwqBmj5IDIyoos3ATSRFBTQyqy5nHjiuZAksxqBcvvtr2HQoPPUqIxENDTQQJuXB9x3\n30L84x+34aOPMhAIkOYtN5eEuZISzWnSZKLjDg6H++vPwc0dF1yghXrv3k0ThMWiCQRpabHNBBy9\noJGTQ8c4VNF48e5ZSUn0trS0aFNBvGPxa5ckzekxEh5BE+8YjVkv5OVpzzFjJJhZrfRbnuuH+2pE\namP199hsTnxtQGxhRm824v93u+k5ao0+PJhjcqfibt1IW3fggHa/e/bUooEi0Ydou1zRyRjjPUNW\nq3HBwhca+rGtrCy+TyAQ/3rbtychTK9RKy6m68rJIcFQP85YLOSgu3Zt9IJtwoS/o7Lye9x8c/zQ\n3ZbmqBU2WorGKgu6dNEGmw4dKHRs0yYyqQwdmngV11gifS+4v4I+VLQl0GtI0tNNYWEjDYsX/xcA\nMGjQWJSUdMc114xQ94v09YjHsGGnx8wUGI9Ek2lBQXRkQiRc2GjfvjzpxBy53WQyqs0TkZcXLWw0\nNJDJgfspcBSFBpv0dFrtWyxIWoFRH7FTVjYZb79NA2D79pofRayJYedOMukBgM12Bs488wz070+r\ntDVrtAiBiRPJTAJEmzeAaHU9X5kBsUPLJYneiVgDXax9DxW5ufGzBcd7Phr77jJGk5rVSv+PdMB0\nOuNnEE7Whkj4K+p2R2tLLBbqQy5s6MNiI+91vFpOZjM9k7w9+ugd/TWYzaRp2r49fj937Jj8PU2E\nosSeoJvir2KzRb8fyerscGI9n3qBoH17WvTwEF+9AMPfA4eD3kWANA78/iaC3/tILVuk02+sNgH0\nLAKxr9Nm097zQ8VRK2wc6qJ2+nCzzEx6kIYMocyHH38MXHhh02yhjYGnGna5WlbY0MPvIz9Hp069\nMH78TDDGUFzcVfWGTk3NineIFjl/LGKppCNX0zxfSXOFjVgsXkyrl44dSbC0WKL37d4deOcdimT4\n+Wd6uTMytHwRX4eL8bpctG9mJtmm47UxO7sAd965AG+//SF++MEKi4XMGlu20CBsMtHvi4q0iBKA\nNGspKcCIESRM+P0UKpmXR+3Ys4cmguxsY0RBS1FeHj3pHk7iRZLFqv4cD0mi/mxoIM3H3r3ayjWW\ndi4ZicaFlBQtYieyDT16xDejuN3aM1dXR78vKjKq+IH4YbJdu2qTYZ8+ycdTfpxY188jNJqLosQ2\nmRUVaWa8eLTEPMCFjYICzcyr90dKSUksRCYKRQY07QSHCw3x/G30z0tmpvbbSGFDS86X+PyHiqNW\n2EhELEk1WoV+cPZQxugYI0eSavPLL4HRo5P+rElkZpKwwVMfJ6Op6khJknQrG1re9es3WjWBtGvX\nAZs3rwJjLK7zJJ/MSkqSC1uxXoqmvihduhgnt/T0HDgcbmRmtmuysBfr3IpCL7fVCnz1FeWRKCqi\nv0Mh7dk6cICEgMxMCqH8/nvScvz4oyYkjRpFatENG2i73U4DDw8PjGxvZuZ49O8/Xk1oNWAAferq\nSOjYsoWc3r77jlbjfMWVlUUr+rw88svQr5h42GKy+xzr2Ym3Kj4YLBbjYNuUZzY7O7o0AXegA7To\nsHi/bSz6iLS0NM2HpLnoJ6rIfsjIIBNTLBKNT2aztrLVHyvW2BdLM2WxaMeP9Wzk5xsnXJ43pKUX\nVHr69iWtAReCIs+lf17S03lYqrY93iSeDH6evDxN2NBrJRp7vHjPs81GmnDeN5HtzM6mMZQ/J/GS\nTsZ7HvRCx2FIHKpyzAkbnTo1Tn0U+aI2l9JSesk/+4wmpUQDXlPhkSIdO5a03EHDvPrqKrXmA4Xj\nkR5VXy6cp/hWFCUqxIvz889kTlq5klZInTo17WWPLG5XVUUTc6dOJFgko7S0B2prd4MxhoICo6MY\ntZ1U/b17G8+TnU2rQR7qxhMdzZ1Lg+xxx9EkvWEDra7efpsmupIS6nM+GPXoQX2ekUHtraqi3zQ0\naPump1MbNm6ke7VmDQ0cRUUkMHChgQtRZ55pvIcpKfS8dutGq+CqKhKI1q2jSaArlVWAy6X9Tq9a\nby5FRXSfnM7kdYEaiz6NvyQlVzXrSU3V8h8AdM87dCAhLJb/Ql4e7d9UbURRUXwB4GBJ9G5kZSWu\nTt1cIotMNoZ27aK/ay1BI56ZTX+v+vYFfvpJe4dNpsZp6hKZYhyO+KaWlBQyHUW2ozlwvxIOv4/8\nX6eTxhHuCxLvfuTlUZsjtT28fTk5B+c7drAcc8LGobZTAZQlccsWStk8Y0bjVlFFRfSbRIwefQ6q\nq6swY8aZ2Lix6e3ijnmxiIwu4ZEcvXppfhq33z5XraLpcMQWNnw+Gpi4JuDnn2lgiOWMF0kgADwa\nLiPSoQOZLXhs+w8/kFbA4aBJNjMzdlbI88+/DdOnU5VFp1NzZOPs3k1pqX/5hSbjoiI6T3o6Hf/t\nt6mdJSWkHZBlLV+AzUZOZgMH0qT14Yc0wa9ZQyu/tDQt3wRjNEhwM4cexkgQyckhTQXPHbBrFxXL\nArQV2oknJr5vFgvdqw4daODt1ClawALofIqi+WwkI9aKyGRqnAN1eXnjhQb9tXXokDxaIhE8hwNf\n8UVOhs2duCkvg9HZMBbFxTRZOZ0UMhyPxk5WRUXNm9hyckj71Zpah5bGatUShsXzmYmcdF2uxCHE\nKSn0bul/1707vdM//0zvuH4cTU2N/4y4XFokUiLiCTzFxZpQENmnOTnUxkjTkc1GY5PLpfl/6GEs\ntrmKHz89nTSmNTWxx4TW5qgUNpI5YR1qGAPOOAN45RUqbHTBBckH6ezs5MKG1WrDtGm3NNv5tLE5\nQGglPwEff1xvCFk9/viJAKj4UqRzpKIAixbRZFFeTv4rubmU8OzLL+nB79mTXh79IKgo5LzIX7hA\ngAaer7+mfA5URpxMEwD5TyxYQAPF2LHRk5rXC/z+O0P79rEHJ/4innIKaV+WLydTxJo1tDL2+2mQ\n37ZNC30bPVpbDXN7diBANTwGDaK/d+1qvGCrKNT+mhpj+mi3m47DTSQ8RDMZPFyRZyuMNUG19MRT\nXBz/vYslBDaG1NSmLw70USD8utu1owm/Of4U8WjfngTcZJqIyDYdDM1dQbeEqedQE6tQJaDdg44d\n6fnu3FlbPHTsSMJGPD+O7OxoUxJfBPD705xFW7x+KSuLb9pIS4uf54Sx+NqmWMJEcXFiYZ63jy8Y\nMjOFsNEiVFTE7+CWNGEkI5YPyJQpwMsvA2+9BZyny6CdKFSusedqaiZBft6mEJkbw2534vnnf8D+\n/d3x2mukxuvXT3shtoXrEPG/CwupWueuXaTy/OormuC7d9dyORw4QPlJAE39P3YsvZS//kovybBh\n9AEoO+CiRTRIvPMOTSoOh2a62LKFVPzcNyIjQ0u7zJjm4V5RQQLO3r3Uvr17NSfOfv002/nevcYJ\nkPezxUKDi9udfFIoLNTuTTKcTtJCcJNRorwHJhP1qdVqnFxawlab7PfNUcW3BvHqHh2Mg6Ie7uxn\nMjVfiIokMrT4YInUnFKVVD9MJpP6aUqOlrYI70+e7h3QclokoiUjn5K9E5Gaic6djZqX/PzYGWOb\nSrJ3jy8CDmXUVyyOOmEj1uqqpIRudEsNDs0lPR2YPJlW9++8Q/Z6k4kmskTq4kTmDo7bHTvPQyJa\nYnVbXt4HS5bQy79nD5UJ79iRtBYAZaDMMxaKRW4ucNllJGhUVpIm4aefKAEal9D79aN/PR7NI3/Y\nMDIz9NHlxJIk6t/evUkI+PFH4JNPaELOzSUhwGYDpk6lc33zjVYsj9tB8/JokLfb6TOBkndi+XLy\noeBJqHhVz169YpsfGptkKjfXKGxEDgLx7MQ8Xb4enuIdoOuIZUs/lnA6NXPewQ7isWiMn1Bz4D5P\nFguNC36/9owUFzfeR6RXrxBkWUYgQDWGGGOQZQU2Gz07oRC9S4rCAJjAmMkghJhMJoRCIQQCAcN3\nfr8fiiLH3P9oQm9mTSZMcP+gxk7iTqcxMsVsbpym8mDJyqJ3oTXeh6Zw1AkbsdAnQUlGawv8hYWU\n0+CttygUccSI5L/hNKZ2RFNo7Dihd7qL5MABUv8XFZGAsWYNCQ58oHQ4tKqYkWRkUMbJvn1JOFix\nQhtUy8ooPwljWjVJgFbt+mPp+ys7m3waePnwtWupHVlZWm2Mjh01DckXX1D7eBGr4mKtbgVAA0+s\nhGyRDlzNgU9aPl+0qaBHuGxKosQ/HP31xxv02rdPbpJLxuH0YtfDi9/FW5kXFlIftkakTHOJHdWk\nwGplapi2Xuuanm5cfDid8QutybIMxhgYY/D7/fD7fbDbSQC12wGHwwJZliFJEqxWK2RZhizLCIVC\n6r/BYAChEAkiskwfmpgYQiEFgQDXGjAwBgSDQfV7EnRNUBQWU2gJBgMGAcXr9UCSNEGHMe13paWm\n8LbDR6dO3GdKQTAYgiyb1PvLSU2VEQopyMw0ITOTNXrO0PdVY75PRLdu8d/JwsLobcnCbw8Fx4Sw\n0RhaWshIdLzyclo9P/UUrWTOOKNxx7RatZTR8Saibdto1T1gAGlEYtVs4Ogny0QCRWlp/GiDTz8l\nvwiewbBbNxIUtm2jNrrdNJlGrtb1f7vdlK0yO5sEgNpaejl4iGFWFv1fH4seif7lkiSoxb8isxry\n9NudO5MmoLJSE15MJuNLmZNDkR2R9tBYiY6SEfk88PPEGgTiPTv8fpSU0CAfeT/iOR5z/594yaya\nQlnZwR8jkpwcWsnH0gzpV9mSJMHv94GxEBTFBIC+49towG49QSNWfyuKAkVREq7wFUWBz+eDJDH4\n/dS5waAPOTmA222C1ysZJmmv1wOPB/D5JPh8DIGAUcMgy7J6vlDID5OJNBWMUVSY0+lQt0e2ix8n\nMlSdCyH8YzabYTaboSiK+p1FZ5/Wf88/wWAIoVAAssy1JyS0mEyagELaQ+qrUEhGMChDlpVwuXa6\njoYGZhBQ9AJJYSGwdWsAfr9i2MYnaquVPjk5QCAQQCDgV4+lPw5jzGBe0m+zWhm8Xi9kOYRAQIGi\ncE0QQ9euJshyUKchAgATAKYKT8GgCcFgEB5PSN1G9yyo9hV9ZwoLgnJ4e/SxIq+RX6fFwoVGpm7n\n8AVTMsHc7T60KwghbBwmKioofPLrr2mQ7dEj/iTD1eSMkbo1VqY+vqrdtYv8E957j9Tu3JwRC/58\nZmaS/TBS2IisEwGQzXHHDprIebEsu53Oo6+8OHassUx0JLyWgf5aHA5je/X5ILKyYgsbyYTEeAIB\nDzm12eILMfpS3JE+MRUVh2/1zPslst2J7kU8B8FEKcX1cIHtYOqRxMNkkpGfH0QoFK2ab2hogMtF\n7wDPY+JwSJAkCcFgCMGgH8GggmAQkGUGxjTh42DU/H6/H6FQSD1Wr16xj9XQUA+zWYEsA4pigslk\nFBwURUFDQwPMZhNsNgaTKaTTOtjCE4Zs0BZYrUBKihlOJ2C1BsAYvz69jd+EYFAOp4i3q5O/zWZr\nlj9GvHvFGIMkSYbaOom+B4yCCO8H/n0swYx/rxdcFEVBMBhEMChDUaBqUWw2hvJyBZKkaWG4WYgE\nLhPKykxhTY8PLhdgNpvC91c2CEJ0PKimJi5AeL30G4fDjIwMi6Ft9H8JNps16lpJ4JJRVARYLArc\nbrp26mMFAIPdbjNcLz3TZlgs2nkURQm3VTFcv17oCYVk2GwIP3d8jiABhoQVhlAoAEnSCzeaENOt\nWwgmkxA2jhnKy2mCWLmS1KYjRsRWhXNhg2+LNZYUFtLEsXEjTZAdOpA2Ys4cWglHOhEdOAC88AIJ\nL+PHRx+PFwGKZPVqChNdsYImsFCItCiZmcYYbrM5eTXLjh3JlMRNJFlZ9LudOxs3AQKx74XdTtcV\nK6Uvh5suGmMeqKigdunTEDc14qklNGetYeLr1ElLepWIg83LEQwGoSiKYfLhBAIBSJIfisLzqjAA\nEmRZhtUK2O1W2Gw2wwTGGFM1UpGmAb8/gFDIH56gNJW9XgCJNSEriqKueAMBmqgUhSEY9KsmBhrM\nTWFhJwiLRYHTaYYkSTEFB1nmTstWuFwWZGRQe4ForYN+spFls1o9Nz3dONlZLBa1/bzNbYlEAkqs\ntvLv4wmG2j2R1XtnDUv6kdu4kBIKyZAkwOl0GtoRuS/X8ugFABIUALvd0iynyrS0lu0X43Mh69pp\nUYUZ/Ta6ByHEEm7oo0CS5ENushLCxmGmrIzU+W+/TSaJ0aOjo2kihQ09PIqDmxv4RNu7Nwkvn38O\nLFxIE+aAAZr5wuEgTcb+/cDrr5PvhL6wV7xJmJcwbteOHDv5Sizyd4wlnxwliYQaLmwwRtoGHkPe\nlHdV396KCrpniYQNfmx+PxINKocqlLqsrPH1GjiMRWuImoLZ3LhzlpcbC0wlIhQKwedrCK+iaIIP\nBn2qdogLAFwLEAwG4HKZYbfbEQqFVKEhEKDJwBaWKuKtviNNAw4HwqvDkDrABgKabwIJV6ZwG7Rj\nBgIkTfEVL5+o9AM1tU9GMOgHYwpsNhMcMTzv9Oc3mUywWLSbHG9S5ZM0QMJ7KMSdk+NrEdqaoNEa\n8PsV6/pjfceJNeEnE4Sor5r+HkbSkv2ify5i0Vztnct1aB05jnhhY/Xq3wFoLztjHvX/a9Y4or5L\nxJo1DthsCrxNWMIlOgc/nscT+3jbt1vhdIYgywxlZU4sW5aKzZtDGDhwPxirV4/tdMpoaDBBlj2Q\nJMDnY9i40R7zvL//no5du6xYs6YOJSVe9O2rYOfOTCxd6sTy5Qq6d69HQYEPdruCHTtKSK52AAAV\nY0lEQVQyMH78Hvz0kxvPPmsHY0C3bgeQlRXEvn1+pKdr8bi8LevXO3HggAW5ufuQmcnwxx8OeL0H\n8OuvMmpqtMdJlj2or5ewfbsViuJRTTax7lfkd3v2WFBdbY66tli/DQaBdesccDplHDigzYayDKxd\nG/1cbN5sg8djAuBRBY6GBhM2btTlXo7DH384IEkKGGv6Ej8QYFi/PnafxWPLFhsaGrSBJNb9kCSg\nUyf6vqWyeB4sDQ31sNsBm80S9rmQwRiZDQBtIg6FNDWxy2U1+AS0FtF+BqTilmWaYOx2q+qwZ01i\nJ0tmE9ezapUDdnv8sSAevDie4NChKMDWrVYEgwHs3t1GPKNbgd8T2blbAabEW8K2cRhj/QCsoL/6\n6bas1P2/X4zvEtEPgAdAUzoh0Tn6AWgAsKoRx0kB4ARwIwAJwEMAeMzobgA5unNYAfSIc947Qfa5\nhQB+BeALt8MNYAiAjgCqAHwLYCiAuwEoAMoBXAggC8AWAO+Efx95neMByADeA7AfQCqAagB+APqy\n9T+EjxtJrPsV6ztT+DzJfisB6B1uS6TXbKznogsAFxr/TLQkPUB9E6eudRTloOeCE9nmfgCCABqZ\nBlRwGOkHek9aMJxMIGgZ+iuK0uoD4hEvbDz33FzoJ5UuXbTV3+rVjqjvErF6NWkiSkoav/pIdI7m\nHO/nn134/vtUWCwK8vN9KC72oksXD/x+BpuN+oqv5mOd98UX89Gt2wFUVDQgLS1kaCNjwI4dVlRW\numC3K7BYZJx/PtksAgGGdevsqKqyYfVqBywWoKTEiz596pCdHcTq1Q6EQsC336YjNTWInj0PICUl\nhLo6CW53CDabjOpqbWVaXq5pM5Ldr8b2E1/p6/fTazaKijTNhqJomhD9sTdtssHrNTX6mWhJmloI\nats2Kw4c0NSnkW3evt2KtLQgnM7kWplk+P0+AMFwlAc5kilKABYLDP4KZBoxQZK00EWKkCCTgdNJ\nqu3mOioerXi9DFarckSlDBcc3fz++++YPn06cIiEjSPejNKlSwUUpUL9W5/wiQ/u+u8SwUO1eObK\nxv4m3jlcLvJtaIoHv6JQ+Oju3ZTWOyeH/tbnlggGNR8D/XlDITrfsGEUiRLZRsbI9j58OP3t8QB9\n+lBWmUCA1MhdulA9D54inBc940WuNm6kyJmiImpbfT3lcair0woTAYkrQCpK8/op1nYeoeB2J84Q\ny3/buTP5hJSWJj5XW6BHD0rUxlXpkdff2Oc6GbIsw+Oph9vNYLFYEAyGEAiQoJqaSukZuS9FKCTD\n7w+p0SE8fM/lAkwm8tKPVwFYIBAcuxwVo0JmpuZk2JZobnp0SaLMmx06AB98ALz0ElX65Nkh403i\nPDQzWUimyZS4VgJjNNF160YJsL79ljJvpqeTsyQ3rWdmkqAB0PfBILWhtrb1k6Pp29oUnM4jQ9AA\nSPjLymp9u73H4wmHYjrCWgn6Xu9gR45z1PEUiiobHDCtVmtCJzaBQHBsc1QIGx06UFheY8MlE9GW\nFmXdulGkyoIFFMI6bBhpJWKN6StXklAAxK8N01RMJsp70aMHVaytrNRyfQDGhFSSRIKHLFMSqUSJ\nqSItd2Zz00qJC5oGzxfBGENDQz0AORwlIoU98GVYLKaYHvrxOBpTVQsEgtajDU2tB0dj8wUkorS0\n6fVTeOGr1iIri6rELllC2oW1a4Fx46L346XXgeRmm3gVFePBmFYavVs34Lff4u9rMjU98RMPVW0O\nyTQbJtOhLcDX0sRLdU25KaSkRbUCgQBCIR7SyWAyKXA6TTCZGILBIAIBymURK3xTIBAIWoqjRtiI\nly+gKXVRmlOqXe8b0RIUF0dPMJJEeTA6d6bMoHPmUFv1ppBAgISB8ePjl+XOzSWh5GCEo5Ys0805\nGG0ST08dWeyNk5PTNuoCNJfIZ4H7TgA+Q86IyMyZXADx+Sg5lcNhV00edrvdkBQqWbptgUAgOFiO\nGmEjFon8EtoqicoF5+UBF15IybTefJNKpjudZObw+8l8Ek/QAKjSaUFB8jbk5ER/16VL00vYx0Jf\npbSliKepSeSkeiigbJZ+Q/0OgCZ4j6ceAIPJJKlJhpJN+HS8BjBGaZvdbqfqN0FOndFJqyRJgdVq\niZvDoqkFoAQCgaA5HNXCxtGIJAFDhpCPw7Jl5EuxciX5rOgrlurp0KHxGom0NM3pU09LaQfKypqf\n7bKptJagwVNvm83mpCYMszkAIIBgEOEiXCYoCmA2K3A4tMqYkZk1I2t7UI0NSpbldtujSnzrU3fr\nBZBQKHlyKoFAIGhthLBxhOJyUYhqRgalJK+uji0kAI2r9sl9A1uiMmgiHA5eSOrIxefzwGql9N28\n+BfXTnDtBdVn8MPhkOByOXWhoxRWyhiDMyzBaUWZ+PYAgkG/WifE5zOHS5JTyfBEmTZjCSACgUBw\nuBHCxhFOSQlw0UXkOJrIBJOMZOGwelwuyq9xLOLxNITzethgMnHNRAh+vy+svQAAqkhKBbgoRble\nEIkUtiLrNUTW9igqkrFzpwKrlcF+qAq1CAQCQQsihI0jFLdbC3FlTCvIdigoL29ctdQjBZ/PZ3Cu\n1OPxUDy1FiYagt3O1MqbZrMZNhsJYPoiYn6/DIsluR9GPPixAUoy16XLoctdIhAIBC2NEDaOUA5n\nOGdjKrq2FtzkkCzks7FQZIcfjOkrkupLkYdgtwOKIiMYVNSy1bHOrddOtLQCQggaAoHgSEYIG4I2\nDa/AySf3QCAAWfaFNSuUmMpsNsfNXqkoCoLBoCEaRA85cQLp6W6D34TfH0AwqMBsBlwuF0wmSsst\nwkQFAoGg6QhhQ9CqkKNkKKFAEA9FUeD11odX9SRYBIPBsJOpTScU+FVfCX0oKWOUuEqWvVAURO1j\nMpmgKDLM5th+E5HChRAyBAKBoHkIYUPQqgQCAdhswbBAQCYKLnjEm7x9Pp+qzSBnTAsURYHfHwBj\nCqxWsxrOyYUCLtTwSA6fD1AUE4JBGS4Xg9vtULUWlDnTr2acjRcaKoQLgUAgaBmEsCFoNUgACMJm\nsyAlxRqe5IPw+73hsE7KfMmFD8YYZFkG4IckadVteblyLlhE+kuYTKYo4UMTLACz2RiWChijPUSV\nUoFAIGhdxCgrOGhipbwmTYQHNpuW+8FqtcJqtcLpVHS+EUEEAgFVEyHLPBOqSz2uXrhojLaBny9R\nPgp9tIdAIBAIWhcx2goOGjJ7BBAKMZhMmpaC56OInPT5RE9hozbViZMLHxRiKkwYAoFAcLQghA3B\nQSPL5BdhsVgQDIbg8wVUE0iylN4ACR8WC2XGFDmrBAKB4OhDCBtNwONpgCwrcfMsHIv4fD4oSghm\nswU2mw02G1QzCc+HIRAIBIJjGzETRKAkSI0pyyHY7TK8Xk/C/Y4lQqEAXC4Y/B+4mUQUABMIBAIB\nIDQbUZD2QobbnRK1zWRisNkkmEwheDz1sNkcTc4dcaQTCATg93tV3wxAgc1mE86WAoFAIIjLManZ\nCAQCcbcpigyHA/B4PDG3S5KElBQX3G4TAoEG+Hy+1mpmmyQUogJjLpcCSfLBahX5KAQCgUCQmGNu\nORoMUp4HWZZhi1GDm0I0GRQlCI/HA7vdrvpncNMJYwwulxMWix/19T40NARhs9mPOC2H3+9X03g3\n1geFsoFKanl04ZchEAgEgmQcc8IGQHkcgkE/FMUaNckqigKz2QKr1Yr6ei+8Xg/sdkc4oyUM+1ut\nVkiSBI/HC4+nAYGARU1AdbgIBoPw+TwwmcxqeGms9oRCISiKD7JMBchipfqOjQxAE6qEoCEQCASC\nZByTwgZjVJXT6/XA4XBGbQPI4dHtdoAxj+qfEQtJkuB2u2C1+uHx+OH1BiFJVrUE+aEmFArB4QDM\nZgV+v1dNlhWZqZOScAFpaU413XcgEEAg4EcgQL/RCx9UR4SqngrHT4FAIBA0hWNS2AAAl8uBUMgD\nn88X05wCaP4ZkuRBfX1DlGZDj9VKAobf70dDgw8ejx9m86EXOkggMMHlcqohqCRIhNRMnbJsQihE\nvilcmLBYLDFSfYfCAgiVXpdlqEXLBAKBQCBoLMessEEaCRv27/chENBSW0eGtHL/DLPZB6/Xn3Ci\nZYzBZrOpQofHw39DYaCHwuQQDAbBmEltDzel2O1GQSIQoOiaSCJTfSuKYvidLIsS6wKBQCBoGsec\nsKEXJqxWK9xuGXV1XgAIayFir9wpYVVsDUgkJpMJdrsdNpsNgUAAXq8ffn8AsizBbLY0KqtmczGZ\nFMQ7tF6QaGymzsjS6wKBQCAQNJVjTtgAYBAo7OFZt67O2+KJuhhjavEx7hPh9Xrh9QJAYgfO5p8T\nCQuQCQQCgUBwqDkmhY1IeHjrgQO+uFqBg0UzZyhhP4ggfD4ueEiQJNreXBMFL2aWyK9EIBAIBILD\ngRA2wthsNphMJng83lb1SdBrO5xOEhAo94cfgYAPsswAaJEjjW2L3+8HY37hwCkQCASCNocQNnTw\nyqOHCn21U4cDauRIMBiC3+9Vo0AoB4YpYQ4MRVFgt5vgcBx5ycUEAoFAcHRzzAkbFBraNlf+XJjg\nlVP1USB+fwChkD8cusrAmKQ6fEqSBFmWIUkmIWgIBAKBoM1xzAkbRwqRUSA8BwYXQGRZRiAQQDCo\nhMNYAcaEY6hAIBAI2h5C2DiC4JoMXmHV4dDyYJBmQ2g1BAKBQND2OOaEjUAgAElq2RDXw4nIgyEQ\nCASCts4xmAqS6nsIBAKBQCA4NBxzmg3KoHkMylgCgUAgEBwmxKwraDPMmzfvcDdB0IKI/jy6EP0p\nOBiaJWwwxq5kjG1gjHkYY98yxgYm2X8UY2wFY8zLGFvDGLsgxj5TGGO/h4/5E2Ps1Oa0TXDkIgaz\nowvRn0cXoj8FB0OThQ3G2DkAHgJwJ4C+AH4C8DFjLDvO/iUA3gPwGYDeAB4F8Dxj7CTdPsMAvA7g\nOQB9ACwA8A5jrFtT25eMlq5/IhAIBAKBIDHN0WxcB+AZRVFeURRlFYBZABoAXBxn/8sBrFcU5WZF\nUVYrivIEgP+Gj8O5BsCHiqL8M7zPHQBWAriqGe1LiKgdIhAIBALBoaVJwgajrFH9QVoKAIBCqoJP\nAQyN87Mh4e16Po7Yf2gj9hEIBAKBQHAE0tRolGwAEoCdEd/vBNAlzm/axdk/lTFmUxTFl2Cfdgna\nYgeA1at/b0SzNXw+D9xuCVartUm/E7Q++/btw8qVKw93MwQthOjPowvRn0cXv/+uzp32Q3G+Izn0\ntQQALr10+mFuhqAl6d+//+FugqAFEf15dCH686ikBMCS1j5JU4WNPQBCAPIivs8DsCPOb3bE2X9/\nWKuRaJ94xwTIzDINwEYA3oStFggEAoFAoMcOEjQ+PhQna5KwoShKgDG2AsAYAAsBgJG35RgAj8X5\n2VIAkWGsJ4e/1+8TeYyTIvaJbEs1KIJFIBAIBAJB02l1jQanOdEo/wRwKWNsBmOsK4CnATgBzAEA\nxtjfGGMv6/Z/GkBHxtj9jLEujLErAEwOH4fzKICxjLHrw/vMBjmi/qsZ7RMIBAKBQNCGaLLPhqIo\nb4ZzatwNMnX8COAURVF2h3dpB6BIt/9Gxtg4AA+DQly3ArhEUZRPdfssZYydB+Cv4c9aABMURfmt\neZclEAgEAoGgrcBEkiuBQCAQCAStiaiNIhAIBAKBoFURwoZAIBAIBIJW5YgUNppaCE5weGCM3ckY\nkyM+v0XsczdjrIox1sAYW8QYK4vYbmOMPcEY28MYq2OM/Zcxlntor+TYhDF2PGNsIWNsW7jvxsfY\n56D7jzGWwRh7jTG2jzG2lzH2PGPM1drXd6yRrD8ZYy/FeF8/iNhH9GcbgTF2K2Pse8bYfsbYTsbY\nfMZY5xj7tYl39IgTNppaCE5w2KkEORK3C3+O4xsYY/8Hqn9zGYBBAOpBfalP7/oIgHEAJgEYAaAA\nwFuHpOUCF8gB/AoAUc5dLdh/rwOoAIW/jwvv90xLXogAQJL+DPMhjO/ruRHbRX+2HY4H8DiAwQBO\nBGAB8AljzMF3aFPvqKIoR9QHwLcAHtX9zUARLjcf7raJT1Rf3QlgZYLtVQCu0/2dCsAD4Gzd3z4A\nE3X7dAEgAxh0uK/vWPqE7/n4lu6/8AAmA+ir2+cUAEEA7Q73dR+tnzj9+RKAtxP8RvRnG/6AyonI\nAI7Tfddm3tEjSrPRzEJwgsNLeVhtu44xNpcxVgQAjLFS0MpJ35f7AXwHrS8HgMKz9fusBrAZor8P\nKy3Yf0MA7FUU5Qfd4T8FrbwHt1b7BXEZFVbJr2KMPckYy9Rt6w/Rn22ZdNB9rgHa3jt6RAkbSFwI\nLlHRNsHh4VsAF4Kk4FkASgH8L2zrawd6WBP1ZR4Af/gFibeP4PDQUv3XDsAu/UZFUUKgAVP08aHl\nQwAzAIwGcDOAkQA+CGeJBqg/RH+2QcJ99AiArxUtP1WbekeP5EJsgjaOoij6nPuVjLHvAWwCcDaA\nVYenVQKBIBaKoryp+/NXxtgvANYBGAXgi8PSKEFjeRJANwDDD3dD4nGkaTaaUwhO0EZQFGUfgDUA\nykD9xZC4L3cAsDLGUhPsIzg8tFT/7QAQ6fkuAciE6OPDiqIoG0BjLo9eEP3ZBmGM/QvAaQBGKYqy\nXbepTb2jR5SwoShKAAAvBAfAUAjukBWUETQPxpgbNHBVhQeyHTD2ZSrIBsj7cgXICUm/TxcAxUhQ\npE/Q+rRg/y0FkM4Y66s7/BjQIPlda7VfkBzGWHsAWQD4BCb6s40RFjQmADhBUZTN+m1t7h093B60\nzfC4PRtAA8i22BUUflMNIOdwt018ovrqQVCIVAcAwwAsAtkCs8Lbbw733RkAegJ4B1QXx6o7xpMA\nNoBUuf0BfAPgq8N9bcfCBxQq2RtAH5A3+p/Dfxe1ZP8B+ADAcgADQWrg1QBePdzXf7R9EvVneNsD\noImoQ3gyWQ7gdwAW0Z9t7xPui72gENg83ceu26fNvKOH/YY18yZfAWAjKIRnKYABh7tN4hOzn+aB\nwpI9IO/m1wGURuwzGxSe1QDgYwBlEdttoFjyPQDqAPwHQO7hvrZj4QNyEJRBpkv958WW7D+QF/1c\nAPvCg+dzAJyH+/qPtk+i/gRgB/ARaCXsBbAewFOIWMSJ/mw7nzh9GQIwI2K/NvGOikJsAoFAIBAI\nWpUjymdDIBAIBALBkYcQNgQCgUAgELQqQtgQCAQCgUDQqghhQyAQCAQCQasihA2BQCAQCAStihA2\nBAKBQCAQtCpC2BAIBAKBQNCqCGFDIBAIBAJBqyKEDYFAIBAIBK2KEDYEAoFAIBC0KkLYEAgEAoFA\n0Kr8f5hs7brIa9JBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efabab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_traffic(app1_ru, 0.03, 2000, seed=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Различия на рынках достаточно существенные, поэтому требуется некоторое время, чтобы приблизиться к значению 0.03.\n",
    "\n",
    "Давайте внимательнее посмотрим, что происходит, когда мы просим модель сделать предсказание:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sampling 0.0752 from market with α=166.000, β=2336.000\n",
      "prior ru->market is 0.075: α=15.035, β=184.965\n",
      "sampling 0.0740 from ru with α=16.035, β=185.965\n",
      "prior app1->ru is 0.074: α=14.804, β=185.196\n",
      "sampling 0.0515 from app1 with α=94.804, β=2107.196\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.051481056835183933"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "app1_ru.sample(silent=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, как мы берем приор у корня дерева (0.07), но он постепенно уменьшается, и так итоге доходит до значения 0.05."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь мы решили показать рекламу 500 раз в приложении 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XGGN2MsZ8AfhYfj3k33OBMeYIY8y2xph9gBuAmcCvRrJR1g6uuNesGVwxzZjh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efb190b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_traffic(app2_ru, 0.02, 500, seed=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На этот раз у нас уже достаточно данных о том, как ведет себя реклама в России, поэтому почти сразу модель начинает выдавать предсказания ближе к реальному CTR."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sampling 0.0643 from market with α=166.000, β=2336.000\n",
      "prior ru->market is 0.064: α=12.863, β=187.137\n",
      "sampling 0.0356 from ru with α=92.863, β=2109.137\n",
      "prior app2->ru is 0.036: α=7.111, β=192.889\n",
      "sampling 0.0229 from app2 with α=20.111, β=681.889\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.022918070152353431"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "app2_ru.sample(silent=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "При такой схеме добавлять новые вершины в граф совсем несложно. Например, мы можем легко добавить еще одну страну:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ua = Node('ua', parent=market)\n",
    "app1_ua = Node('app1', parent=ua)\n",
    "app2_ua = Node('app2', parent=ua)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Так как данных по этой стране ещё нет, то при решении модель руководствуемся данными от родительских вершин.\n",
    "Сделаем семпл из одной из новых вершин и сравним его с другими вершинами:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HDhzQuwtCB0b5uktYEMKAesLCUIch4kHDDzaGw2F8vjh2+9U4HO6015LJI4RC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\nht7vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efe7db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "sns.distplot(app1_us.sample_multiple(50), label='app1 us')\n",
    "sns.distplot(app1_ru.sample_multiple(50), label='app1 ru')\n",
    "sns.distplot(app1_ua.sample_multiple(100), label='app1 ua')\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Так как данных в этих вершинах у нас еще нет, то данные мы берём из родителя. Разброс, который мы тут получаем, регулируется параметром `downsample_size` - именно он позволяет указать, каким сильным будет влияние родителя на ребенка. В теории этот параметр мы называли $n$. Чем $n$ выше - тем больше влияние родителя на детей. Можно поменять его и посмотреть, что будет:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ua.downsample_size = 5000\n",
    "app1_ua.downsample_size = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h5QYiwiLYe26vT58rhBDC9T4Lc4DvAXOBHOBG4A+KopSoqrq6J4E89dRTWCyWNtfmzZvH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0efc3f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "sns.distplot(app1_us.sample_multiple(50), label='app1 us')\n",
    "sns.distplot(app1_ru.sample_multiple(50), label='app1 ru')\n",
    "sns.distplot(app1_ua.sample_multiple(100), label='app1 ua')\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом случае влияние выше, поэтому дисперсия ниже, и значения сильнее сконцентрированы вокруг среднего значения родителя. Однако такой приор будет сложнее \"побить\" - потребуется много данных, чтобы статистика самой вершины начала преобладать над приором."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Bandit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Но это у нас не совсем бандит получился - а просто иерархическая модель. Конечно, можно представить, что это всё-таки был бандит, а руки - это все возможные комбинации признаков. В ситуации с покупкой траффика из конкретного приложения (тот пример, который мы рассматривали выше) это может даже работать: мы дергаем за \"руку\", находим наиболее многообещающую комбинацию, покупаем показы, обновляем статистику и так повторяем пока не закончатся деньги. \n",
    "\n",
    "В ситуации с RTB всё немного иначе. Допустим, мы DSP и кроме \"Horns & Hooves Ltd\" у нас есть много других клиентов. Для каждого клиента мы проводим рекламную кампанию по продвижению их приложения.\n",
    "\n",
    "Вот приходит с биржи запрос, в котором говорится, что приложение - это \"Angry Birds\", страна США и ещё что-нибудь. То есть получается, что признаки зафиксированы, мы никак не можем их поменять, поэтому это не рука, а что-то, что мы не контролируем. Но мы можем выбрать, какую именно кампанию использовать для того, чтобы отреагировать на входящий запрос. То есть мы можем рассматривать кампании, как руки бандита, и дёргать (то есть показывать) именно ту кампанию, которая по нашему с бандитом мнению наиболее многообещающая. \n",
    "\n",
    "Как это реализовать? Есть несколько вариантов.\n",
    "\n",
    "Первый вариант - добавить кампанию как признак на какой-нибудь из уровней иерархической модели. Это может быть любой уровень, он может идти сразу после корня, может идти после страны, или даже быть в самом конце. Приходит запрос - мы подставляем значения всех кампаний, которые мы знаем, а потом ту \"дёргаем\" кампанию, для которой вывод был наибольший. \n",
    "\n",
    "Второй вариант - создать индивидуальную модель на каждую кампанию. Тогда берём семпл из каждой модели и выбираем кампанию с наибольшим значением. Прямо как обычный бандит, только рука у нас сложнее, с иерархией. \n",
    "\n",
    "Для этого варианта, да и частично для первого, есть проблема - что делать, когда мы начинаем новую кампанию? Тут тоже можно проявить креативность. Например, можно взять кампанию, которая больше всего похожа на нашу, сделать копию модели, и использовать её. При этом можно обнулить статистики в листьях, чтобы они не сильно мешали изучать среду. Можно взять среднее всех сущесвующих кампаний, тоже обнулить статистику в листьях. Можно обнулять не только листья, но и родителей этих листев, и даже родителей родителей. \n",
    "\n",
    "Реализовывать это мы тут не будем, вроде не должно быть сильно сложно."
   ]
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    "Естественно, не получится просто взять код выше и запустить в прод. Есть несколько моментов, над которыми нужно подумать, прежде чем это делать. \n",
    "\n",
    "Например:\n",
    "\n",
    "- Разговаривать со всеми родительскими вершинами может быть долго, особенно если граф получается большой. Поэтому можно каким-либо образом заранее насемлить значений для каждого листа (например, используя функцию `sample_multiple`), а потом обновлять модель сразу батчем, например, каждые 20 минут.\n",
    "- Если бандит работает какое-то продолжительное время, то он узнает много информации, которую неплохо было бы забывать с течением времени. Поэтому клики, которым больше недели, можно выкинуть. Существует много способов это сделать - например пересчитывать параметры в вершинах или добавлять exponential decay. Второе я никогда не пробовал, а первое можно довольно легко реализовать.\n",
    "- Писать это лучше не на питоне, а на чём-нибудь типа C++ или Java. Кстати, семплер для beta из scipy довольно медленный, есть более эффективные реализации. \n",
    "\n",
    "На этом, пожалуй, всё. Не забываем ставить плюсики."
   ]
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    "## Источники и ссылки\n",
    "\n",
    "- Multi-Armed Bandits: https://dataorigami.net/blogs/napkin-folding/79031811-multi-armed-bandits\n",
    "- Understanding Bayes: Updating priors via the likelihood: https://alexanderetz.com/2015/07/25/understanding-bayes-updating-priors-via-the-likelihood/\n",
    "- Bayesian hierarchical modeling: https://en.wikipedia.org/wiki/Bayesian_hierarchical_modeling\n",
    "- A Tutorial on Thompson Sampling: https://arxiv.org/abs/1707.02038\n",
    "- Display Advertising with Real-Time Bidding (RTB) and Behavioural Targeting: https://arxiv.org/abs/1610.03013\n",
    "- Machine Learning: The High Interest Credit Card of Technical Debt: https://research.google.com/pubs/pub43146.html "
   ]
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